Abstract
For any group G, π e (G) denotes the set of orders of its elements. If Ω is a subset of positive integers, h(Ω) stands for the number of isomorphism classes of finite groups G such that π e (G) = Ω. Let Ω = π e (PGL(2, p)), where p ≥ 5 is a prime number. In this paper, we prove that h(Ω) ∈ {1, ∞ }.
2000 Mathematics Subject Classification:
Acknowledgments
This project was supported by the National Science Foundation of China (Grant No. 10171074), Jiangsu Natural Science Foundation (Grant No. BK200133). The first author would like to thank the University authority sincerely for the partial support of this article.
Notes
#Communicated by D. Easdown.