Abstract
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 get a new characterization of, where Q 8 is the Quaternion group of order 8. We get the theorem following: Theorem. Let G be a non-abelian group, G≅Q 8 if and only if τe(G) = τe(Q 8) = {1,6}.
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