论文标题
在$ n $ centralizer $ ca $ -groups上
On $n$-centralizer $CA$-groups
论文作者
论文摘要
令$ g $为有限的非阿布尔集团，$ m = | g |/| z（g）| $。在本文中，我们调查了$ m $ $ $ $ g $带有环状中心的，我们将证明，如果$ g $是有限的非亚伯利亚$ m $ m $ m $ - 中心化合物$ ca $ - ca $ - ca $ - 组，那么$ m = 2^r。子组$ g'$是订单2的，然后存在一个整数$ s> 1 $，这样$ m = 2^{2s}。
Let $G$ be a finite non-abelian group and $m=|G|/|Z(G)|$. In this paper we investigate $m$-centralizer group $G$ with cyclic center and we will prove that if $G$ is a finite non-abelian $m$-centralizer $CA$-group, then there exists an integer $r>1$ such that $m=2^r.$ It is also prove that if $G$ is an $m$-centralizer non-abelian finite group which is not a $CA$-group and its derived subgroup $G'$ is of order 2, then there exists an integer $s>1$ such that $m=2^{2s}.$
