论文标题
计算有限组中2个元素子集的中心化数量
Counting the Number of Centralizers of 2-Element Subsets in a Finite Group
论文作者
论文摘要
假设$ g $是一个有限的组。 $ g $的所有$ 2- $元素子集的所有中心化的集合用$ 2美分（g）$表示。组$ g $称为$（2，n） - $ centralizer如果$ | 2分（g）| = n $和原始$（2，n） - $ centralizer如果$ | 2分（g）| = | 2分钟（\ frac {g} {z（g）}）| = n $，其中$ z（g）$表示$ g $的中心。本文的目的是介绍$（2，n）的主要属性 - $ centralizer Groups的特征为$（2，n） - $ centralizer and opentive $（2，n） - $ centralizer offer，$ n \ leq 9 $。
Suppose $G$ is a finite group. The set of all centralizers of $2-$element subsets of $G$ is denoted by $2-Cent(G)$. A group $G$ is called $(2,n)-$centralizer if $|2-Cent(G)| = n$ and primitive $(2,n)-$centralizer if $|2-Cent(G)| = |2-Cent(\frac{G}{Z(G)})| = n$, where $Z(G)$ denotes the center of $G$. The aim of this paper is to present the main properties of $(2,n)-$centralizer groups among them a characterization of $(2,n)-$centralizer and primitive $(2,n)-$centralizer groups, $n \leq 9$, are given.
