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Proceedings of the American Mathematical Society

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

 

 

On relative normal complements in finite groups. II


Author: Henry S. Leonard
Journal: Proc. Amer. Math. Soc. 88 (1983), 212-214
MSC: Primary 20D40
DOI: https://doi.org/10.1090/S0002-9939-1983-0695243-6
MathSciNet review: 695243
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Abstract: Given a finite group $ G$ and subgroups $ H$ and $ {H_0}$ with $ {H_0} \triangleleft H$, we let $ \pi $ denote the set of prime divisors of $ (H:{H_0})$, and we denote this configuration by $ (G,H,{H_0},\pi )$. Pamela Ferguson has shown that if $ H/{H_0}$ is solvable, then under certain conditions there exists a unique relative normal complement $ {G_0}$ of $ H$ over $ {H_0}$. In this paper we give alternative proofs of her two theorems.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0695243-6
Keywords: Finite groups, normal complement, $ \pi $-subgroups
Article copyright: © Copyright 1983 American Mathematical Society