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Published online by Cambridge University Press: 06 November 2024
In this article, we study rational matrix representations of VZ p-groups (p is any prime). Using our findings on VZ p-groups, we explicitly obtain all inequivalent irreducible rational matrix representations of all p-groups of order $\leq p^4$. Furthermore, we establish combinatorial formulae to determine the Wedderburn decompositions of rational group algebras for VZ p-groups and all p-groups of order
$\leq p^4$, ensuring simplicity in the process.
The first author acknowledges University Grants Commission, Government of India. The corresponding author acknowledges SERB, Government of India for financial support through grant (MTR/2019/000118).
Communicated by Benjamin Martin