p-Divisibility of the number of linear representations of an Abelian p-group

Chen Wang

doi:10.1016/j.jcta.2019.04.005

paper

p-Divisibility of the number of linear representations of an Abelian p-group

arXiv:1709.04829 · doi:10.1016/j.jcta.2019.04.005

Abstract

We establish lower bounds for the $p$ -divisibility of the quantity $# Hom (G, G L_{n} (F_{q}))$ , the number of homomorphisms from $G$ to a general linear group, where $G$ is an Abelian $p$ -group. This is in analogy to the result of Krattenthaler and Müller \cite{MR3383810} on homomorphisms to symmetric groups.