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RATIONAL REPRESENTATIONS AND RATIONAL GROUP ALGEBRA OF VZ
$\boldsymbol {p}$-GROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 06 November 2024, pp. 1-30
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- Article
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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.
