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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
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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
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  • [6] Ernest Shult, On a class of doubly transitive groups, Illinois J. Math. 16 (1972), 434–445. MR 0296150

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Article copyright: © Copyright 1973 American Mathematical Society