Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


References [Enhancements On Off] (What's this?)

  • [1] M. Aschbacher, Finite groups with a proper $ 2$-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

Similar Articles

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