Base sizes for finite linear groups with solvable stabilisers

2024/08/16 by Anton A. Baykalov, Baykalov, Anton A. · 1 citation
Mathematics · #20D06 #20D60 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2408.08510

openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a transitive permutation group on a finite set with solvable point stabiliser and assume that the solvable radical of G is trivial. In 2010, Vdovin conjectured that the base size of G is at most 5. Burness proved this conjecture in the case of primitive G. The problem was reduced by Vdovin in 2012 to the case when G is an almost simple group. Now the problem is further reduced to groups of Lie type through work of Baykalov and Burness. In this paper, we prove the strong form of the conjecture for all almost simple groups with socle isomorphic to \PSL_n(q), and the remaining classical groups will be handled in two forthcoming papers.

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