On EPO-groups with a given property on their conjugacy classes

Abstract

Let G be a finite group and V(G) be the set of all non-central conjugacy classes of G. Consider the conjugacy class graph $\Gamma (G)$ of G which is defined as follows: its vertex set is the set V(G) and two distinct vertices x^G and y^G are connected with an edge if o(x) and o(y) are not coprime. In this article, we determine the structure of groups G whose non-trivial elements have prime orders and whose graph $\Gamma (G)$ does not have any complete subgraph with six vertices.

Keywords:

• EPO-group
• Frobenius group
• conjugacy class graph

2020 Mathematics Subject Classification:

• Primary: 20E45
• Secondary: 20D60

Acknowledgment

The authors would like to thank the referees for carefully reading the manuscript and for giving constructive comments which substantially helped improving the quality of the article.