有限$p$群非正规子群的正规闭包

Finite $p$-Groups and Normal Closures of Nonnormal Subgroups

中文关键词:  非正规子群  正规闭包  戴德金$p$群

英文关键词:nonnormal subgroups  normal closures  Dedekindian $p$-groups

中文摘要:

      本文分类了$G/H^G$循环的有限$p$群$G$, 其中$H$为$G$的任意极小非正规子群, $H^G$ 为$H$在$G$中的正规闭包.

英文摘要:

      In this paper, finite $p$-groups $G$ with $G/H^G$ being cyclic for every minimal nonnormal subgroup $H$ are classified up to isomorphism, where $H^G$ denotes the normal closure of $H$.