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.
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).