On Subgroups Generated by Small Classes in Finite Groups

Abstract

Let G be a finite group and M(G) be the subgroup of G generated by all noncentral elements of G that lie in the conjugacy classes of the smallest size. Recently several results have been proved regarding the nilpotency class of M(G) and F(M(G)), where F(M(G)) denotes the Fitting subgroup of M(G). We prove some conditional results regarding the nilpotency class of M(G).

Key Words:

• Conjugacy class
• Fitting subgroup
• Nilpotency class
• Solvable

2010 Mathematics Subject Classification:

• Primary 20D25
• Secondary 20E45

ACKNOWLEDGMENTS

I thank Prof. E. C. Dade for his useful comments and suggestions.

Notes

Communicated by A. Olshanskii.