Geodesic
Abelian supplements in almost simple groups
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e14

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Let G be an almost simple group with socle $G_0$. In this paper we prove that whenever $G/G_0$ is abelian, then there exists an abelian subgroup A of G such that $G=AG_0$. We propose a few applications of this structural property of almost simple groups. 
Costantini, Mauro; Lucchini, Andrea; Nemmi, Daniele. Abelian supplements in almost simple groups. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e14. doi: 10.1017/fms.2024.160
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