A new characterization of A5

Let G be a group and τe(G) the set of numbers of elements of G of the same order. In this paper, by τe(G), we give a new characterization of A5, where A5 is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, $${G\cong A_5}$$ if and only if τe(G) = τe(A5) = {1, 15, 20, 24}.