A characterization of $$A_5$$ by same-order type |
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| Authors: | Email author" target="_blank">Rulin?ShenEmail author Xuan?Zou Wujie?Shi |
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| Institution: | 1.Department of Mathematics,Hubei University for Nationalities,Enshi,People’s Republic of China;2.Key Laboratory of Group and Graph Theories and Applications,Chongqing University of Arts and Sciences,Chongqing,People’s Republic of China |
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| Abstract: | For a group G, write \(g \sim h\) if \(g, h \in G\) have the same order. The set of sizes of the equivalence classes with respect to this relation is called the same-order type of G; thus it is the set with numbers of elements of each order. In this article we prove that a group is isomorphic to the alternating group \(A_5\) if and only if the same-order type of G is \(\{1,pq,4p,8q\}\) with the p and q primes. |
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