On the regular Sylow p-subgroups of Chevalley groups over $$\mathbb{Z}_{p^m } $$

Abstract

We prove that a Sylow p-subgroup of the general linear group of dimension n over the residue ring modulo pm is regular for n2 < p and powerful if and only if n = 2 and m = 1. We obtain similar results for the Sylow p-subgroups of normal types over the same ring.