On the Unitary Subgroups of group algebras

2020/04/22 by Balogh, Zsolt Adam
#FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2004.10806

Abstract

Let FG be the group algebra of a finite p-group G over a finite field F of characteristic p and * the classical involution of FG. The *-unitary subgroup of FG, denoted by V_*(FG), is defined to be the set of all normalized units u satisfying the property u^*=u^-1. In this paper we give a recursive method how to compute the order of the *-unitary subgroup for many non-commutative group algebras. We also prove a variant of the modular isomorphism question of group algebras, where F is a finite field of characteristic two, that is V_*(FG) determines the basic group G for all non-abelian 2-groups G of order at most 2⁴.

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