On Conjugacy Class Graph of Normal Subgroup  

作　　者：Ruifang Chen Xianhe Zhao 

机构地区：[1]College of Mathematics and Information Science,Henan Normal University Xinxiang,Henan 453007,China

出　　处：《Algebra Colloquium》2022年第3期437-442,共6页代数集刊（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(11901169);the Youth Science Foundation of Henan Normal University(2019QK02);the Project for Graduate Education Reform and Quality Improvement of Henan Province and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,College of Mathematics and Information Science.

摘　　要：Let G be a finite group and N a normal subgroup of G.Denote by Γ_(G)(N)the graph whose vertices are all distinct G-conjugacy class sizes of non-central elements in N,and two vertices of Γ_(G)(N)are adjacent if and only if they are not coprime numbers.We prove that if the center Z(N)=Z(G)∩N and Γ_(G)(N)is k-regular for k≥1,then either a section of Nis a quasi-Frobenius group or Γ_(G)(N)is a complete graph with k+1 vertices.

关 键 词：normal subgroup conjugacy class size quasi-Frobenius group GRAPH 

分 类 号：O152[理学—数学]