Year: 2025
Type: article
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 ) \mathrm{PSL}_{n}(q) , and the remaining classical groups will be handled in two forthcoming papers.
Source: Journal of Group Theory
Author: Anton A. Baykalov
Institution: Ollscoil na Gaillimhe – University of Galway
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Australian Research Council
OpenAlex ID: W4407677712