TY - JOUR
AU - V. Laver
AU - Z. Balogh
PY - 2020/05/25
Y2 - 2022/10/07
TI - Unitary subgroups of commutative group algebras of characteristic two
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 6
SE - Research articles
DO - 10.37863/umzh.v72i6.1068
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1068
AB - UDC 512.552.7Let $FG$ 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.
ER -