Rational Representations and Rational Group Algebra of VZ p-groups

2023/08/19 by Ram Karan Choudhary, Choudhary, Ram Karan, Sunil Kumar Prajapati +1
Engineering · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2308.09981

openalex publication_date 2023/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study rational matrix representations of VZ p-groups (p is any prime). Utilizing our findings on VZ p-groups, we explicitly obtain all inequivalent irreducible rational matrix representations of all p-groups of order ≤ p⁴. Furthermore, we establish combinatorial formulas to determine the Wedderburn decompositions of rational group algebras for VZ p-groups and all p-groups of order ≤ p⁴, ensuring simplicity in the process.

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