ON UNITARY SUBGROUPS OF GROUP ALGEBRAS

Authors : Zsolt Adam BALOGH

Pages : 187-198

Doi:10.24330/ieja.852199

View : 16 | Download : 13

Publication Date : 2021-01-05

Article Type : Research Paper

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 $V_*insert ignore into journalissuearticles values(FG);$, 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