The Coexponent of a Finite p-Group

Abstract

In this paper,we present a sharp bound for the nilpotency class of a finite p-group (where p is an odd prime) in terms of its coexponent. As to a powerful p-group,we give the sharp bound for the nilpotency class in terms of its coexponent for arbitrary prime p.

Key Words:

• Finite p-group
• Nilpotency class
• Coexponent
• Powerful p-group

Acknowledgments

The authors are supported by RFDP and National 973 project. The second author is also partially supported by the NKBRSF of China (No. G19980306).