A characterization of \(A_5\) by same-order type

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• 作者：Rulin Shen ; Xuan Zou ; Wujie Shi
• 关键词：Finite groups ; Element orders ; Same ; order types
• 刊名：Monatshefte für Mathematik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：182
• 期：1
• 页码：127-142
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：182

文摘

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.