The characterization of almost simple groups PGL(2, p) by their element orders

摘要

For any group G, pi(e)(G) denotes the set of orders of its elements. If Omega is a subset of positive integers, h(Omega) stands for the number of isomorphism classes of finite groups G such that pi(e)(G) = Omega. Let Omega = pi(e)(PGL(2, p)), where p greater than or equal to 5 is a prime number. In this paper, we prove that h(Omega) is an element of {1, infinity}.