A condition for the existence of a strongly embedded subgroup

Author:
Michael Aschbacher

Journal:
Proc. Amer. Math. Soc. **38** (1973), 509-511

MSC:
Primary 20D25; Secondary 05C25

DOI:
https://doi.org/10.1090/S0002-9939-1973-0318308-0

MathSciNet review:
0318308

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Abstract: Let be a normal set of involutions in a finite group. Form the involutory graph with vertex set by joining distinct commuting elements of . Assume the product of any two such elements is in , and the graph is disconnected. Then the group generated by contains a strongly embedded subgroup. Two corollaries are proved.

**[1]**M. Aschbacher,*Finite groups with a proper -generated core*(to appear).**[2]**H. Bender,*Transitive Gruppen gerader Ordung in deven jede Involution genau einere Punkt festalt*, J. Algebra**17**(1971), 527-554. MR**0288172 (44:5370)****[3]**W. Feit,*The current situation in the theory of finite simple groups*, Proc. Internat. Congress Math. (Nice, 1970), vol. 1, Gauthier-Villars, Paris, 1971, pp. 55-93. MR**0427449 (55:481)****[4]**C. Hering,*On subgroups with trivial normalizer intersection*, J. Algebra**20**(1972), 622-629. MR**0322020 (48:385)****[5]**E. Shult,*On the fusion of an involution in its centralizer*(to appear).**[6]**-,*On a class of doubly transitive groups*, Illinois J. Math.**16**(1972), 434-445. MR**0296150 (45:5211)**

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0318308-0

Article copyright:
© Copyright 1973
American Mathematical Society