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arXiv · 1810.05350

A Criterion for the Existence of a Solvable $\pi$-Hall Subgroup in a Finite Group

A. A. Buturlakin·A. P. Khramova
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Abstract

Let $G$ be a finite group and let $\pi$ be a set of primes. In this paper, we prove a criterion for the existence of a solvable $\pi$-Hall subgroup of $G$, precisely, the group $G$ has a solvable $\pi$-Hall subgroup if, and only if, $G$ has a $\{p,q\}$-Hall subgroup for any pair $p$, $q\in\pi$.

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A. A. Buturlakin, A. P. Khramova. 2018-10-12. A Criterion for the Existence of a Solvable $\pi$-Hall Subgroup in a Finite Group. https://arxiv.org/abs/1810.05350

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