$p$-Parts of Stabilizers in Primitive Permutation Groups
Group Theory
2026-03-24 v1 Representation Theory
Abstract
Let G be a primitive permutation group on a finite set Omega. Let p^2 divide |G|, for a prime p. We show that when G is solvable, there exists a subset of Omega whose stabilizer S has the property that 1<|S|_p<|G|_p. We offer a counting argument which should be helpful when G is not solvable.
Cite
@article{arxiv.2603.21001,
title = {$p$-Parts of Stabilizers in Primitive Permutation Groups},
author = {David Gluck},
journal= {arXiv preprint arXiv:2603.21001},
year = {2026}
}