2025/09/27 by Choudhary, Ram Karan, Prajapati, Sunil Kumar
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2509.23349
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 p5 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.