Unitary subgroups of commutative group algebras of characteristic two

• Дата: 2020
• Автори: Laver, V., Balogh, Z., Лавер, В., Балог, Ж.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2020
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/1068
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.