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


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318308-0
Article copyright: © Copyright 1973 American Mathematical Society

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