标题： 关于阶数为$p^5$的群在$\mathbb{Q}$上的矩阵表示 显示英文标题

标题： On Matrix Representations of Groups of Order $p^5$ over $\mathbb{Q}$

摘要： In this article, we determine all inequivalent irreducible rational matrix representations of groups of order $p^5$, where $p$ is an odd prime. We also derive combinatorial formulations for the Wedderburn decomposition of rational group algebras of these $p$-groups, using results from their rational representations. 显示英文摘要

摘要： In this article, we determine all inequivalent irreducible rational matrix representations of groups of order $p^5$, where $p$ is an odd prime. We also derive combinatorial formulations for the Wedderburn decomposition of rational group algebras of these $p$-groups, using results from their rational representations.