ON UNITARY SUBGROUPS OF GROUP ALGEBRAS

Year 2021, Volume: 29 Issue: 29, 187 - 198, 05.01.2021

Zsolt Adam Balogh

https://doi.org/10.24330/ieja.852199

Cited By: 6

Abstract

Let $FG$ be the group algebra of a finite $p$-group $G$ over a
finite field $F$ of characteristic $p$ and let $*$ be 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 certain non-commutative group algebras.
A variant of the modular isomorphism question of group algebras is
also considered.

Keywords

Group ring, group of units, unitary subgroup

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