Characterization of 3D4(q)
Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Guiyun [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2002 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Hong Kong 2001 |
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| Übergeordnetes Werk: |
Enthalten in: Southeast Asian bulletin of mathematics - Springer-Verlag, 1977, 25(2002), 3 vom: Feb., Seite 389-401 |
|---|---|
| Übergeordnetes Werk: |
volume:25 ; year:2002 ; number:3 ; month:02 ; pages:389-401 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10012-001-0389-2 |
|---|
| Katalog-ID: |
OLC2051517371 |
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| 520 | |a Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). | ||
| 650 | 4 | |a Finite Group | |
| 650 | 4 | |a Simple Group | |
| 650 | 4 | |a Prime Graph | |
| 650 | 4 | |a Finite Simple Group | |
| 650 | 4 | |a Order Component | |
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10.1007/s10012-001-0389-2 doi (DE-627)OLC2051517371 (DE-He213)s10012-001-0389-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Guiyun verfasserin aut Characterization of 3D4(q) 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Hong Kong 2001 Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). Finite Group Simple Group Prime Graph Finite Simple Group Order Component Enthalten in Southeast Asian bulletin of mathematics Springer-Verlag, 1977 25(2002), 3 vom: Feb., Seite 389-401 (DE-627)130026042 (DE-600)424019-4 (DE-576)034180419 0129-2021 nnns volume:25 year:2002 number:3 month:02 pages:389-401 https://doi.org/10.1007/s10012-001-0389-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_4277 AR 25 2002 3 02 389-401 |
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10.1007/s10012-001-0389-2 doi (DE-627)OLC2051517371 (DE-He213)s10012-001-0389-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Guiyun verfasserin aut Characterization of 3D4(q) 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Hong Kong 2001 Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). Finite Group Simple Group Prime Graph Finite Simple Group Order Component Enthalten in Southeast Asian bulletin of mathematics Springer-Verlag, 1977 25(2002), 3 vom: Feb., Seite 389-401 (DE-627)130026042 (DE-600)424019-4 (DE-576)034180419 0129-2021 nnns volume:25 year:2002 number:3 month:02 pages:389-401 https://doi.org/10.1007/s10012-001-0389-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_4277 AR 25 2002 3 02 389-401 |
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10.1007/s10012-001-0389-2 doi (DE-627)OLC2051517371 (DE-He213)s10012-001-0389-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Guiyun verfasserin aut Characterization of 3D4(q) 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Hong Kong 2001 Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). Finite Group Simple Group Prime Graph Finite Simple Group Order Component Enthalten in Southeast Asian bulletin of mathematics Springer-Verlag, 1977 25(2002), 3 vom: Feb., Seite 389-401 (DE-627)130026042 (DE-600)424019-4 (DE-576)034180419 0129-2021 nnns volume:25 year:2002 number:3 month:02 pages:389-401 https://doi.org/10.1007/s10012-001-0389-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_4277 AR 25 2002 3 02 389-401 |
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10.1007/s10012-001-0389-2 doi (DE-627)OLC2051517371 (DE-He213)s10012-001-0389-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Guiyun verfasserin aut Characterization of 3D4(q) 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Hong Kong 2001 Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). Finite Group Simple Group Prime Graph Finite Simple Group Order Component Enthalten in Southeast Asian bulletin of mathematics Springer-Verlag, 1977 25(2002), 3 vom: Feb., Seite 389-401 (DE-627)130026042 (DE-600)424019-4 (DE-576)034180419 0129-2021 nnns volume:25 year:2002 number:3 month:02 pages:389-401 https://doi.org/10.1007/s10012-001-0389-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_4277 AR 25 2002 3 02 389-401 |
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10.1007/s10012-001-0389-2 doi (DE-627)OLC2051517371 (DE-He213)s10012-001-0389-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Guiyun verfasserin aut Characterization of 3D4(q) 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Hong Kong 2001 Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). Finite Group Simple Group Prime Graph Finite Simple Group Order Component Enthalten in Southeast Asian bulletin of mathematics Springer-Verlag, 1977 25(2002), 3 vom: Feb., Seite 389-401 (DE-627)130026042 (DE-600)424019-4 (DE-576)034180419 0129-2021 nnns volume:25 year:2002 number:3 month:02 pages:389-401 https://doi.org/10.1007/s10012-001-0389-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_4277 AR 25 2002 3 02 389-401 |
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Characterization of 3D4(q) |
| abstract |
Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). © Springer-Verlag Hong Kong 2001 |
| abstractGer |
Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). © Springer-Verlag Hong Kong 2001 |
| abstract_unstemmed |
Abstract The author defined the concept “order components” in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree $ groups^{[10]} $; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that: Theorem 1.Let G be a finite group, M =3D4(q). If G and M has the same order components, then G ≅ M. And the following theorems follows from Theorem 1. Theorem 2. (Thompson’s Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G ≅ M. (ref. [6]) Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, $ π_{e} $(G) = $ π_{e} $(M), then G ≅ M. (ref. [15]) All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]). © Springer-Verlag Hong Kong 2001 |
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| title_short |
Characterization of 3D4(q) |
| url |
https://doi.org/10.1007/s10012-001-0389-2 |
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| doi_str |
10.1007/s10012-001-0389-2 |
| up_date |
2024-07-04T04:38:02.107Z |
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7.400923 |