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.
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.
