Unitary subgroups of commutative group algebras of characteristic two

Abstract

UDC 512.552.7

Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^{\circledast}=u^{-1}$. In this paper we establish the order of $V_{\circledast}(FG)$ for all involutions $\circledast$ which arise from $G$, where $G$ is a finite cyclic $2$-group and show that all $\circledast$-unitary subgroups of $FG$ are not isomorphic.

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Published
25.05.2020
How to Cite
LaverV., and BaloghZ. “Unitary Subgroups of Commutative Group Algebras of Characteristic Two”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 6, May 2020, pp. 751-7, doi:10.37863/umzh.v72i6.1068.
Section
Research articles