Minimal groups of given representation dimension

Jonathan Cohen

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arXiv · 2206.10752

Minimal groups of given representation dimension

Jonathan Cohen

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Abstract

For a finite group $G$, let $\text{rdim}(G)$ denote the smallest dimension of a faithful, complex linear representation of $G$. It is clear that $\text{rdim}(H)\leq \text{rdim}(G)$ for any subgroup $H$ of $G$. We consider $G$ with the property that $\text{rdim}(H)<\text{rdim}(G)$ whenever $H$ is a proper subgroup of $G$, in particular proving a classification of such groups when $G$ is abelian or $\text{rdim}(G)\leq 3$.

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Jonathan Cohen. 2022-06-21. Minimal groups of given representation dimension. https://arxiv.org/abs/2206.10752

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