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arXiv · 1709.04829

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

Chen Wang
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Abstract

We establish lower bounds for the $p$-divisibility of the quantity $\#\operatorname{Hom}(G,GL_n(\mathbb{F}_q))$, 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.

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Chen Wang. 2017-09-14. p-Divisibility of the number of linear representations of an Abelian p-group. https://doi.org/10.1016/j.jcta.2019.04.005

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