A Criterion for the Existence of a Solvable π-Hall Subgroup in a Finite Group

2018/10/12 by Buturlakin, A. A., Khramova, A. P.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1810.05350

Abstract

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

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