Counting the number of centralizers of 2-element subsets in a finite group

摘要

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 vertical bar 2 - Cent(G)vertical bar = n and primitive (2,n)-centralizer if vertical bar 2 - Cent(G)vertical bar = vertical bar 2 - Cent(G/Z(G)vertical bar= n, where Z(G) denotes the center of G. The aim of this z(G) 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 <= 9, are given.