Let $K$ be field of characteristic 2 and let $G$ be a finite non-abelian2-group with the cyclic derived subgroup $G'$, and there exists a centralelement $z$ of order 2 in $Z(G) \backslash G'$. We prove that the unit group ofthe group algebra $KG$ possesses a section isomorphic to the wreath product ofa group of order 2 with the derived subgroup of the group $G$, giving for suchgroups a positive answer to the question of A. Shalev.
展开▼
机译：令$ K $为特征2的字段，令$ G $为具有循环派生子组$ G'$的有限非abelian2-群，并且在$ Z（G）中存在阶数为2的中心元素$ z $。反斜线G'$。我们证明，代数$ KG $的单位组具有与第$ 2 $组的派生子组第2阶组的花环积同构的截面，从而为此类组提供了对A. Shalev问题的肯定答案。
展开▼
