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RATIONAL REPRESENTATIONS AND RATIONAL GROUP ALGEBRA OF VZ $\boldsymbol {p}$-GROUPS

Published online by Cambridge University Press:  06 November 2024

RAM KARAN CHOUDHARY
Affiliation:
Indian Institute of Technology, Bhubaneswar, Arugul Campus, Jatni, Khurda 752050, India e-mail: [email protected]
SUNIL KUMAR PRAJAPATI*
Affiliation:
Indian Institute of Technology, Bhubaneswar, Arugul Campus, Jatni, Khurda 752050, India

Abstract

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.

Type
Research Article
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

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

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