Унiтарнi пiдгрупи комутативних групових алгебр характеристики 2

В. Лавер; Ж.  Балог

doi:10.37863/umzh.v72i6.1068

Authors

V. Laver Uzhhorod National University https://orcid.org/0000-0001-6627-2445
Z. Balogh Budapest Business School, University of Applied Science, Budapest, Hungary https://orcid.org/0000-0001-5908-3443

DOI:

https://doi.org/10.37863/umzh.v72i6.1068

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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Unitary subgroups of commutative group algebras of characteristic two

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