Finite Groups with a Disconnected p-Regular Conjugacy Class Graph

Abstract

Let G be a finite p-solvable group for a fixed prime p. Attach to G a graph Γ _p (G) whose vertices are the non-central p-regular conjugacy classes of G and connect two vertices by an edge if their cardinalities have a common prime divisor. In this note we study the structure and arithmetical properties of the p-regular class sizes in p-solvable groups G having Γ _p (G) disconnected.

Key Words:

• Finite groups; Conjugacy classes; P-Regular elements; Graphs

Mathematics Subject Classification:

• 20E45
• 20D20

Acknowledgment

The authors would like to thank the referee for his/her valuable supervision which corrected errors in the original manuscript.

Notes

^#Communicated by A. Turull.