On sharp characters of type {−1, 0, 2}

Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be...
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Autor*in:	Abdollahi, Alireza [verfasserIn] Bagherian, Javad Ebrahimi, Mahdi Khatami, Maryam Shahbazi, Zahra Sobhani, Reza

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	sharp character sharp pair finite group

Anmerkung:	© Institute of Mathematics, Czech Academy of Sciences 2022

Übergeordnetes Werk:	Enthalten in: Czechoslovak mathematical journal - New York, NY [u.a.] : Springer Science + Business Media B.V., 1951, 72(2022), 4 vom: 06. Okt., Seite 1081-1087
Übergeordnetes Werk:	volume:72 ; year:2022 ; number:4 ; day:06 ; month:10 ; pages:1081-1087

Links:	Volltext

DOI / URN:	10.21136/CMJ.2022.0356-21

Katalog-ID:	SPR048799971

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100	1		\|a Abdollahi, Alireza \|e verfasserin \|4 aut
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520			\|a Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12.
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700	1		\|a Bagherian, Javad \|4 aut
700	1		\|a Ebrahimi, Mahdi \|4 aut
700	1		\|a Khatami, Maryam \|4 aut
700	1		\|a Shahbazi, Zahra \|4 aut
700	1		\|a Sobhani, Reza \|4 aut
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912			\|a GBV_ILN_74
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912			\|a GBV_ILN_95
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912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
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912			\|a GBV_ILN_4324
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912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
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912			\|a GBV_ILN_4338
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allfields	10.21136/CMJ.2022.0356-21 doi (DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e DE-627 ger DE-627 rakwb eng Abdollahi, Alireza verfasserin aut On sharp characters of type {−1, 0, 2} 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213 Bagherian, Javad aut Ebrahimi, Mahdi aut Khatami, Maryam aut Shahbazi, Zahra aut Sobhani, Reza aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 06. Okt., Seite 1081-1087 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087 https://dx.doi.org/10.21136/CMJ.2022.0356-21 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 06 10 1081-1087
spelling	10.21136/CMJ.2022.0356-21 doi (DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e DE-627 ger DE-627 rakwb eng Abdollahi, Alireza verfasserin aut On sharp characters of type {−1, 0, 2} 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213 Bagherian, Javad aut Ebrahimi, Mahdi aut Khatami, Maryam aut Shahbazi, Zahra aut Sobhani, Reza aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 06. Okt., Seite 1081-1087 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087 https://dx.doi.org/10.21136/CMJ.2022.0356-21 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 06 10 1081-1087
allfields_unstemmed	10.21136/CMJ.2022.0356-21 doi (DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e DE-627 ger DE-627 rakwb eng Abdollahi, Alireza verfasserin aut On sharp characters of type {−1, 0, 2} 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213 Bagherian, Javad aut Ebrahimi, Mahdi aut Khatami, Maryam aut Shahbazi, Zahra aut Sobhani, Reza aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 06. Okt., Seite 1081-1087 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087 https://dx.doi.org/10.21136/CMJ.2022.0356-21 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 06 10 1081-1087
allfieldsGer	10.21136/CMJ.2022.0356-21 doi (DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e DE-627 ger DE-627 rakwb eng Abdollahi, Alireza verfasserin aut On sharp characters of type {−1, 0, 2} 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213 Bagherian, Javad aut Ebrahimi, Mahdi aut Khatami, Maryam aut Shahbazi, Zahra aut Sobhani, Reza aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 06. Okt., Seite 1081-1087 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087 https://dx.doi.org/10.21136/CMJ.2022.0356-21 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 06 10 1081-1087
allfieldsSound	10.21136/CMJ.2022.0356-21 doi (DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e DE-627 ger DE-627 rakwb eng Abdollahi, Alireza verfasserin aut On sharp characters of type {−1, 0, 2} 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213 Bagherian, Javad aut Ebrahimi, Mahdi aut Khatami, Maryam aut Shahbazi, Zahra aut Sobhani, Reza aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 06. Okt., Seite 1081-1087 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087 https://dx.doi.org/10.21136/CMJ.2022.0356-21 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 06 10 1081-1087
language	English
source	Enthalten in Czechoslovak mathematical journal 72(2022), 4 vom: 06. Okt., Seite 1081-1087 volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087
sourceStr	Enthalten in Czechoslovak mathematical journal 72(2022), 4 vom: 06. Okt., Seite 1081-1087 volume:72 year:2022 number:4 day:06 month:10 pages:1081-1087
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	sharp character sharp pair finite group
isfreeaccess_bool	false
container_title	Czechoslovak mathematical journal
authorswithroles_txt_mv	Abdollahi, Alireza @@aut@@ Bagherian, Javad @@aut@@ Ebrahimi, Mahdi @@aut@@ Khatami, Maryam @@aut@@ Shahbazi, Zahra @@aut@@ Sobhani, Reza @@aut@@
publishDateDaySort_date	2022-10-06T00:00:00Z
hierarchy_top_id	327082755
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language_de	englisch
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If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. 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author	Abdollahi, Alireza
spellingShingle	Abdollahi, Alireza misc sharp character misc sharp pair misc finite group On sharp characters of type {−1, 0, 2}
authorStr	Abdollahi, Alireza
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topic_title	On sharp characters of type {−1, 0, 2} sharp character (dpeaa)DE-He213 sharp pair (dpeaa)DE-He213 finite group (dpeaa)DE-He213
topic	misc sharp character misc sharp pair misc finite group
topic_unstemmed	misc sharp character misc sharp pair misc finite group
topic_browse	misc sharp character misc sharp pair misc finite group
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	On sharp characters of type {−1, 0, 2}
ctrlnum	(DE-627)SPR048799971 (SPR)CMJ.2022.0356-21-e
title_full	On sharp characters of type {−1, 0, 2}
author_sort	Abdollahi, Alireza
journal	Czechoslovak mathematical journal
journalStr	Czechoslovak mathematical journal
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author_browse	Abdollahi, Alireza Bagherian, Javad Ebrahimi, Mahdi Khatami, Maryam Shahbazi, Zahra Sobhani, Reza
container_volume	72
format_se	Elektronische Aufsätze
author-letter	Abdollahi, Alireza
doi_str_mv	10.21136/CMJ.2022.0356-21
title_sort	on sharp characters of type {−1, 0, 2}
title_auth	On sharp characters of type {−1, 0, 2}
abstract	Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. © Institute of Mathematics, Czech Academy of Sciences 2022
abstractGer	Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. © Institute of Mathematics, Czech Academy of Sciences 2022
abstract_unstemmed	Abstract For a complex character χ of a finite group G, it is known that the product %${\rm{sh}}\left( \chi \right) = \prod\limits_{l \in L\left( \chi \right)} {\left( {\chi \left( 1 \right) - l} \right)} %$ is a multiple of ∣G∣, where L(χ) is the image of χ on G − {1} The character χ is said to be a sharp character of type L if L = L(χ) and sh(χ) = ∣G∣. If the principal character of G is not an irreducible constituent of χ, then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type {−1, 0, 2}. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. © Institute of Mathematics, Czech Academy of Sciences 2022
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title_short	On sharp characters of type {−1, 0, 2}
url	https://dx.doi.org/10.21136/CMJ.2022.0356-21
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author2	Bagherian, Javad Ebrahimi, Mahdi Khatami, Maryam Shahbazi, Zahra Sobhani, Reza
author2Str	Bagherian, Javad Ebrahimi, Mahdi Khatami, Maryam Shahbazi, Zahra Sobhani, Reza
ppnlink	327082755
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doi_str	10.21136/CMJ.2022.0356-21
up_date	2024-07-03T21:33:07.891Z
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