On the converse of Hall's theorem

Xiaoyu Chen

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arXiv · 1508.00250

On the converse of Hall's theorem

Xiaoyu Chen

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Abstract

In this paper, we mainly investigate the converse of a well-known theorem proved by P. Hall, and present detailed characterizations under the various assumptions of the existence of some families of Hall subgroups. In particular, we prove that if $p\neq 3$ and a finite group $G$ has a Hall $\{p,q\}$-subgroup for every prime $q\neq p$, then $G$ is $p$-soluble.

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Xiaoyu Chen. 2015-08-02. On the converse of Hall's theorem. https://arxiv.org/abs/1508.00250

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