On the divisibility of $#\Hom(\Gamma,G)$ by $|G|
Group Theory
2018-03-30 v1 Combinatorics
Abstract
We extend and reformulate a result of Solomon on the divisibility of the title. We show, for example, that if is a finitely generated group, then divides #\Hom(\Gamma,G) for every finite group if and only if has infinite abelianization. As a consequence we obtain some arithmetic properties of the number of subgroups of a given index in such a group .
Keywords
Cite
@article{arxiv.1105.6066,
title = {On the divisibility of $#\Hom(\Gamma,G)$ by $|G|},
author = {Fernando Rodriguez Villegas and Cameron Gordon},
journal= {arXiv preprint arXiv:1105.6066},
year = {2018}
}