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.
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.