Abstract
In a finite group G, denotes the product of element orders of G. Let and t be prime numbers. Recently, it was proved that , Cpq, and Cpqrs are characterizable by the product of element orders, and if , then or . In this paper, we continue this work and we show that (for p > 5) and Cpqrst are characterizable by the product of element orders. In the rest of the paper, we show that if then and . This shows that the structure of uniquely determined and so is the only group with this form of .
Acknowledgments
The authors would like to thank the referee for valuable comments and suggestions which improved the manuscript seriously.