发表机构
United Arab Emirates University（阿联酋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对换位子群阶为$p$的有限奇素数$p$-群$G$的群代数，证明其李幂零指数由斜对称元构成的李子代数决定，并描述了该子代数的下李中心序列结构。
AI 中文摘要
设$FG$是有限$p$-群$G$在特征为$p$的有限域$F$上的群代数，其中$p$为奇素数；设$*$为$FG$的经典对合，$FG^-$为$FG$中关于$*$的斜对称元构成的李子代数。本文证明：当$G$的换位子群阶为$p$时，$FG$的李幂零指数由其李子代数$FG^-$决定，同时还描述了$FG^-$的下李中心序列各项的结构。
英文摘要
Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$, where $p$ is an odd prime. Let $*$ be the classical involution of $FG$ and let $FG^-$ be the Lie subalgebra of the skew symmetric elements with respect to $*$. In this paper, we prove that the Lie nilpotency index of $FG$ is determined by its Lie subalgebra $FG^-$, in the case when $G$ is a $p$-group with a commutator subgroup of order $p$. The structure of the terms of the lower Lie central series of $FG^-$ has also been described.
CommentsAccepted for publication in Carpathian Mathematical Publications
