A condition for the existence of a strongly embedded subgroup
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- by Michael Aschbacher PDF
- Proc. Amer. Math. Soc. 38 (1973), 509-511 Request permission
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
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M. Aschbacher, Finite groups with a proper $2$-generated core (to appear).
- Helmut Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt, J. Algebra 17 (1971), 527–554 (German). MR 288172, DOI 10.1016/0021-8693(71)90008-1
- 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
- Christoph Hering, On subgroups with trivial normalizer intersection, J. Algebra 20 (1972), 622–629. MR 322020, DOI 10.1016/0021-8693(72)90075-0 E. Shult, On the fusion of an involution in its centralizer (to appear).
- Ernest Shult, On a class of doubly transitive groups, Illinois J. Math. 16 (1972), 434–445. MR 296150
Additional Information
- © Copyright 1973 American Mathematical Society
- 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