On the base size of a transitive group with solvable point stabilizer

TL;DR

This paper establishes an upper bound on the base size of certain transitive groups with solvable stabilizers, linking it to automorphism groups of composition factors, advancing understanding of permutation group structure.

Contribution

It provides a new bound on the base size of transitive groups with solvable point stabilizers, based on automorphisms of composition factors, extending previous results.

Findings

Bound on base size for groups with solvable stabilizers

Connection between base size and automorphisms of composition factors

Conditions involving the solvable radical and composition factors

Abstract

We prove that the base size of a transitive group $G$ with solvable point stabilizer and with trivial solvable radical is not greater than $k$ provided the same statement holds for the group of $G$-induced automorphisms of each nonabelian composition factor of $G$.