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

MathSciNet review:
0318308

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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]**Helmut Bender,*Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt*, J. Algebra**17**(1971), 527–554 (German). MR**0288172****[3]**Walter Feit,*The current situation in the theory of finite simple groups*, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 55–93. MR**0427449****[4]**Christoph Hering,*On subgroups with trivial normalizer intersection*, J. Algebra**20**(1972), 622–629. MR**0322020****[5]**E. Shult,*On the fusion of an involution in its centralizer*(to appear).**[6]**Ernest Shult,*On a class of doubly transitive groups*, Illinois J. Math.**16**(1972), 434–445. MR**0296150**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
20D25,
05C25

Retrieve articles in all journals with MSC: 20D25, 05C25

Additional Information

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

Article copyright:
© Copyright 1973
American Mathematical Society