On standard subgroups of type $^{2}E_{6}(2)$
HTML articles powered by AMS MathViewer
- by G. Stroth PDF
- Proc. Amer. Math. Soc. 81 (1981), 365-368 Request permission
Abstract:
The purpose of this paper is to close one of the last gaps in the classification of finite simple groups containing a standard subgroup. We prove that a simple group containing a standard subgroup of type ${}^2{E_6}(2)$ has to be isomorphic to ${F_2}$, the baby monster.References
- Michael Aschbacher, A characterization of Chevalley groups over fields of odd order, Ann. of Math. (2) 106 (1977), no. 2, 353–398. MR 498828, DOI 10.2307/1971100
- Michael Aschbacher and Gray M. Seitz, On groups with a standard component of known type, Osaka Math. J. 13 (1976), no. 3, 439–482. MR 435200
- George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403–420. MR 202822, DOI 10.1016/0021-8693(66)90030-5
- David M. Goldschmidt, $2$-fusion in finite groups, Ann. of Math. (2) 99 (1974), 70–117. MR 335627, DOI 10.2307/1971014
- Marshall Hall Jr., Simple groups of order less than one million, J. Algebra 20 (1972), 98–102. MR 285603, DOI 10.1016/0021-8693(72)90090-7
- D. F. Holt, Transitive permutation groups in which an involution central in a Sylow $2$-subgroup fixes a unique point, Proc. London Math. Soc. (3) 37 (1978), no. 1, 165–192. MR 575516, DOI 10.1112/plms/s3-37.1.165
- Arthur Reifart, On finite simple groups with large extraspecial subgroups. I, J. Algebra 53 (1978), no. 2, 452–470. MR 502644, DOI 10.1016/0021-8693(78)90291-0
- Gary M. Seitz, Chevalley groups as standard subgroups. I, Illinois J. Math. 23 (1979), no. 1, 36–57. MR 516569
- Robert Steinberg, Automorphisms of finite linear groups, Canadian J. Math. 12 (1960), 606–615. MR 121427, DOI 10.4153/CJM-1960-054-6
- Gernot Stroth, Eine Kennzeichnung der Gruppe $^{2}E_{6}(2^{n})$, J. Algebra 35 (1975), 534–547 (German). MR 376848, DOI 10.1016/0021-8693(75)90065-4
- G. Stroth, A characterization of Fischer’s sporadic simple group of the order $2^{41}\cdot 3^{13}\cdot 5^{6}\cdot 7^{2}\cdot 11\cdot 13\cdot 17\cdot 19\cdot 23\cdot 31\cdot 47$, J. Algebra 40 (1976), no. 2, 499–531. MR 417277, DOI 10.1016/0021-8693(76)90208-8
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 365-368
- MSC: Primary 20D05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0597641-6
- MathSciNet review: 597641