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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Hall subgroups and $p$-solvability
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by A. Gonçalves and C. Y. Ho PDF
Proc. Amer. Math. Soc. 52 (1975), 97-98 Request permission

Abstract:

Let $G$ be a finite group and let $\pi (G) = \{ p,{q_1}, \ldots ,{q_r}\}$ be the set of all prime divisors of $G$. Suppose there is a $p’$-Hall subgroup $H$. If there are subgroups $P,{Q_1}, \ldots ,{Q_r}$ such that $P\epsilon {\operatorname {Syl} _p}(G),{Q_i}\epsilon {\operatorname {Syl} _{{q_i}}}(H)$, and ${L_i} = P{Q_i}$ is a subgroup, $i = 1, \ldots ,r$, then $G$ is $p$-solvable. Moreover, if the subgroup $H$ is solvable, then $G$ is solvable too.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 97-98
  • MSC: Primary 20D10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0372022-6
  • MathSciNet review: 0372022