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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On relative normal complements in finite groups. II
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by Henry S. Leonard PDF
Proc. Amer. Math. Soc. 88 (1983), 212-214 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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