On soluble subgroups of sporadic groups

2021/05/03 by Burness, Timothy C. · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2105.00718

Abstract

Let G be an almost simple sporadic group and let H be a soluble subgroup of G. In this paper we prove that there exists x,y ∈ G such that H ∩ H^x ∩ H^y=1, which is equivalent to the bound b(G,H) \leqslant 3 with respect to the base size of G on the set of cosets of H. This bound is best possible. In this setting, our main result establishes a strong form of a more general conjecture of Vdovin on the intersection of conjugate soluble subgroups of finite groups. The proof uses a combination of computational and probabilistic methods.

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