Set-stabilizers in solvable permutation groups

TL;DR

This paper investigates the structure of set-stabilizers in finite solvable permutation groups, showing that after factoring out a certain elementary abelian 3-subgroup, some stabilizer is a 2-group.

Contribution

It establishes a new structural property of set-stabilizers in solvable groups, linking elementary abelian 3-subgroups to 2-group stabilizers.

Findings

Existence of a normal elementary abelian 3-subgroup in G

Some set-stabilizer in G is a 2-group after factoring out this subgroup

Provides insight into the subgroup structure of solvable permutation groups

Abstract

Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.