Rational Representations and Rational Group Algebra of VZ p-groups
Ram Karan Choudhary, Sunil Kumar Prajapati

TL;DR
This paper classifies all irreducible rational matrix representations of VZ p-groups and small p-groups, providing explicit formulas for their group algebra decompositions, advancing understanding of their algebraic structure.
Contribution
It explicitly determines all inequivalent irreducible rational matrix representations of p-groups of order up to p^4 and derives combinatorial formulas for their Wedderburn decompositions.
Findings
Complete classification of irreducible rational representations for small p-groups.
Explicit formulas for Wedderburn decompositions of rational group algebras.
Simplified process for analyzing algebraic structures of VZ p-groups.
Abstract
In this article, we study rational matrix representations of VZ -groups ( is any prime). Utilizing our findings on VZ -groups, we explicitly obtain all inequivalent irreducible rational matrix representations of all -groups of order . Furthermore, we establish combinatorial formulas to determine the Wedderburn decompositions of rational group algebras for VZ -groups and all -groups of order , ensuring simplicity in the process.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Topics in Algebra · graph theory and CDMA systems
