论文标题
给定代表维度的最小群体
Minimal groups of given representation dimension
论文作者
论文摘要
对于有限的组$ g $，令$ \ text {rdim}（g）$表示忠实，复杂的线性表示$ g $的最小维度。显然，对于任何$ g $的任何子组$ h $，$ \ text {rdim}（h）\ leq \ text {rdim}（g）$。我们将$ g $与属性一起考虑$ \ text {rdim}（h）<\ text {rdim}（g）$，每当$ h $是$ g $的适当子组时，尤其是当$ g $是$ g $的分类为abelian或$ \ text {rdim}（rdim}（rdim}（rdim}（g）\ leq 3 $时
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 $\text{rdim}(G)\leq 3$.
