Isomorphism problem of Unitary Subgroups of Group Algebras

2019/08/11 by Zsolt Balogh, Balogh, Zsolt, Victor Bovdi +1
Computer Science · Engineering · Mathematics · #16S34 #16U60 #20C05 #20D15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1908.03877

openalex publication_date 2019/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V_* be the normalized unitary subgroup of the modular group algebra FG of a finite p-group G over a finite field F with the classical involution *. We investigate the isomorphism problem for the group V_*, that asks when the group V_* is determined by its group algebra FG. We confirm it for classes of finite abelian p-groups, 2-groups of maximal class and non-abelian 2-groups of order at most 16.

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