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<p>In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of nested GVZ <i>p</i>-groups, where <i>p</i> is an odd prime. Using this formula, we derive an explicit combinatorial expression for the Wedderburn decomposition of rational group algebras of all two-generator <i>p</i>-groups of class 2. Additionally, we provide explicit combinatorial formulas for the Wedderburn decomposition of rational group algebras of certain families of nested GVZ <i>p</i>-groups with arbitrarily large nilpotency class. We also classify all nested GVZ <i>p</i>-groups of order at most <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p^5\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mn>5</mn> </msup> </math></EquationSource> </InlineEquation> and compute the Wedderburn decomposition of their rational group algebras. Finally, we determine a complete set of primitive central idempotents for the rational group algebras of nested GVZ <i>p</i>-groups.</p>

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A combinatorial technique for the Wedderburn decomposition of rational group algebras of nested GVZ p-groups

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Ram Karan Choudhary,
  • Sunil Kumar Prajapati

摘要

In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of nested GVZ p-groups, where p is an odd prime. Using this formula, we derive an explicit combinatorial expression for the Wedderburn decomposition of rational group algebras of all two-generator p-groups of class 2. Additionally, we provide explicit combinatorial formulas for the Wedderburn decomposition of rational group algebras of certain families of nested GVZ p-groups with arbitrarily large nilpotency class. We also classify all nested GVZ p-groups of order at most \(p^5\) p 5 and compute the Wedderburn decomposition of their rational group algebras. Finally, we determine a complete set of primitive central idempotents for the rational group algebras of nested GVZ p-groups.