Let G be an almost simple group with socle. In this paper we prove that whenever G/G0 is abelian, then there exists an abelian subgroup A of G such that G = AG0. We propose a few applications of this structural property of almost simple groups.
Abelian supplements in almost simple groups
Costantini M.;Lucchini A.;Nemmi D.
2025
Abstract
Let G be an almost simple group with socle. In this paper we prove that whenever G/G0 is abelian, then there exists an abelian subgroup A of G such that G = AG0. We propose a few applications of this structural property of almost simple groups.
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