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Proceedings of the American Mathematical Society

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

 

 

Complements to solvable Hall subgroups


Author: Robert Gilman
Journal: Proc. Amer. Math. Soc. 27 (1971), 241-243
MSC: Primary 20.43
DOI: https://doi.org/10.1090/S0002-9939-1971-0269742-7
MathSciNet review: 0269742
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Abstract: A Hall subgroup $ H$ of a finite group $ G$ is a subgroup whose order is relatively prime to its index. We show that if $ H$ is solvable and if the way prime power elements of $ H$ are conjugate in $ G$ is restricted, then $ G$ has a quotient isomorphic to $ H$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0269742-7
Keywords: Solvable Hall subgroup, normal complement, finite group, quotient group, $ c$-closed, transfer, prime power, fusion
Article copyright: © Copyright 1971 American Mathematical Society