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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Hall subgroup normalizers and character correspondences in $ M$-groups


Author: I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 109 (1990), 647-651
MSC: Primary 20C15; Secondary 20D10
MathSciNet review: 1017004
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Abstract: Let $ H$ be a Hall subgroup of an $ M$-group $ G$, and let $ N$ be its normalizer in $ G$. It is shown that the group $ N/H'$ is an $ M$-group. This involves the construction of an explicit bijection between the sets of irreducible characters of $ G$ and of $ N$ with degrees coprime to the order of $ H$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1017004-4
PII: S 0002-9939(1990)1017004-4
Article copyright: © Copyright 1990 American Mathematical Society