On a class of finite solvable groups
Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a g...
Ausführliche Beschreibung
Autor*in: |
Beidleman, James C. [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2013 |
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Schlagwörter: |
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Anmerkung: |
© Versita Warsaw and Springer-Verlag Wien 2013 |
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Übergeordnetes Werk: |
Enthalten in: Central European journal of mathematics - Berlin : Springer, 2003, 11(2013), 9 vom: 04. Juni, Seite 1598-1604 |
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Übergeordnetes Werk: |
volume:11 ; year:2013 ; number:9 ; day:04 ; month:06 ; pages:1598-1604 |
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DOI / URN: |
10.2478/s11533-013-0264-2 |
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Katalog-ID: |
SPR020660278 |
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520 | |a Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. | ||
650 | 4 | |a -permutable subgroup |7 (dpeaa)DE-He213 | |
650 | 4 | |a PST-group |7 (dpeaa)DE-He213 | |
650 | 4 | |a Normalizer |7 (dpeaa)DE-He213 | |
650 | 4 | |a X-group |7 (dpeaa)DE-He213 | |
700 | 1 | |a Heineken, Hermann |4 aut | |
700 | 1 | |a Schmidt, Jack |4 aut | |
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10.2478/s11533-013-0264-2 doi (DE-627)SPR020660278 (SPR)s11533-013-0264-2-e DE-627 ger DE-627 rakwb eng Beidleman, James C. verfasserin aut On a class of finite solvable groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Versita Warsaw and Springer-Verlag Wien 2013 Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. -permutable subgroup (dpeaa)DE-He213 PST-group (dpeaa)DE-He213 Normalizer (dpeaa)DE-He213 X-group (dpeaa)DE-He213 Heineken, Hermann aut Schmidt, Jack aut Enthalten in Central European journal of mathematics Berlin : Springer, 2003 11(2013), 9 vom: 04. Juni, Seite 1598-1604 (DE-627)358627508 (DE-600)2097190-4 1644-3616 nnns volume:11 year:2013 number:9 day:04 month:06 pages:1598-1604 https://dx.doi.org/10.2478/s11533-013-0264-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2013 9 04 06 1598-1604 |
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10.2478/s11533-013-0264-2 doi (DE-627)SPR020660278 (SPR)s11533-013-0264-2-e DE-627 ger DE-627 rakwb eng Beidleman, James C. verfasserin aut On a class of finite solvable groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Versita Warsaw and Springer-Verlag Wien 2013 Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. -permutable subgroup (dpeaa)DE-He213 PST-group (dpeaa)DE-He213 Normalizer (dpeaa)DE-He213 X-group (dpeaa)DE-He213 Heineken, Hermann aut Schmidt, Jack aut Enthalten in Central European journal of mathematics Berlin : Springer, 2003 11(2013), 9 vom: 04. Juni, Seite 1598-1604 (DE-627)358627508 (DE-600)2097190-4 1644-3616 nnns volume:11 year:2013 number:9 day:04 month:06 pages:1598-1604 https://dx.doi.org/10.2478/s11533-013-0264-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2013 9 04 06 1598-1604 |
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10.2478/s11533-013-0264-2 doi (DE-627)SPR020660278 (SPR)s11533-013-0264-2-e DE-627 ger DE-627 rakwb eng Beidleman, James C. verfasserin aut On a class of finite solvable groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Versita Warsaw and Springer-Verlag Wien 2013 Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. -permutable subgroup (dpeaa)DE-He213 PST-group (dpeaa)DE-He213 Normalizer (dpeaa)DE-He213 X-group (dpeaa)DE-He213 Heineken, Hermann aut Schmidt, Jack aut Enthalten in Central European journal of mathematics Berlin : Springer, 2003 11(2013), 9 vom: 04. Juni, Seite 1598-1604 (DE-627)358627508 (DE-600)2097190-4 1644-3616 nnns volume:11 year:2013 number:9 day:04 month:06 pages:1598-1604 https://dx.doi.org/10.2478/s11533-013-0264-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2013 9 04 06 1598-1604 |
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10.2478/s11533-013-0264-2 doi (DE-627)SPR020660278 (SPR)s11533-013-0264-2-e DE-627 ger DE-627 rakwb eng Beidleman, James C. verfasserin aut On a class of finite solvable groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Versita Warsaw and Springer-Verlag Wien 2013 Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. -permutable subgroup (dpeaa)DE-He213 PST-group (dpeaa)DE-He213 Normalizer (dpeaa)DE-He213 X-group (dpeaa)DE-He213 Heineken, Hermann aut Schmidt, Jack aut Enthalten in Central European journal of mathematics Berlin : Springer, 2003 11(2013), 9 vom: 04. Juni, Seite 1598-1604 (DE-627)358627508 (DE-600)2097190-4 1644-3616 nnns volume:11 year:2013 number:9 day:04 month:06 pages:1598-1604 https://dx.doi.org/10.2478/s11533-013-0264-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2013 9 04 06 1598-1604 |
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10.2478/s11533-013-0264-2 doi (DE-627)SPR020660278 (SPR)s11533-013-0264-2-e DE-627 ger DE-627 rakwb eng Beidleman, James C. verfasserin aut On a class of finite solvable groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Versita Warsaw and Springer-Verlag Wien 2013 Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. -permutable subgroup (dpeaa)DE-He213 PST-group (dpeaa)DE-He213 Normalizer (dpeaa)DE-He213 X-group (dpeaa)DE-He213 Heineken, Hermann aut Schmidt, Jack aut Enthalten in Central European journal of mathematics Berlin : Springer, 2003 11(2013), 9 vom: 04. Juni, Seite 1598-1604 (DE-627)358627508 (DE-600)2097190-4 1644-3616 nnns volume:11 year:2013 number:9 day:04 month:06 pages:1598-1604 https://dx.doi.org/10.2478/s11533-013-0264-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2013 9 04 06 1598-1604 |
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author-letter |
Beidleman, James C. |
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10.2478/s11533-013-0264-2 |
title_sort |
on a class of finite solvable groups |
title_auth |
On a class of finite solvable groups |
abstract |
Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. © Versita Warsaw and Springer-Verlag Wien 2013 |
abstractGer |
Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. © Versita Warsaw and Springer-Verlag Wien 2013 |
abstract_unstemmed |
Abstract A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms. © Versita Warsaw and Springer-Verlag Wien 2013 |
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container_issue |
9 |
title_short |
On a class of finite solvable groups |
url |
https://dx.doi.org/10.2478/s11533-013-0264-2 |
remote_bool |
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author2 |
Heineken, Hermann Schmidt, Jack |
author2Str |
Heineken, Hermann Schmidt, Jack |
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doi_str |
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up_date |
2024-07-03T17:27:17.747Z |
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