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Proceedings of the American Mathematical Society

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

 

 

Counterexamples on the fusion of involutions in finite groups


Author: Stephen Doro
Journal: Proc. Amer. Math. Soc. 59 (1976), 23-24
MSC: Primary 20D05
DOI: https://doi.org/10.1090/S0002-9939-1976-0409626-9
MathSciNet review: 0409626
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Abstract: Some examples are given of simple groups $ G$ containing a conjugacy class of involutions $ \mathcal{C}$ such that if $ S$ is a Sylow $ 2$-subgroup of $ G$, then there exist subgroups $ A \subseteq B \subseteq S$ with $ \vert A:B\vert = 2$ and $ \mathcal{C} \cap S \subseteq B - A$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0409626-9
Keywords: Involutions, fusion, Sylow $ 2$-subgroups, $ {Z^{\ast}}$ theorem
Article copyright: © Copyright 1976 American Mathematical Society