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A new characterization of A 5

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Abstract

Let G be a group and τ e (G) the set of numbers of elements of G of the same order. In this paper, by τ e (G), we give a new characterization of A 5, where A 5 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 τ e (G) = τ e (A 5) = {1, 15, 20, 24}.

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Correspondence to Wujie Shi.

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Communicated by D. Segal.

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Shen, R., Shao, C., Jiang, Q. et al. A new characterization of A 5 . Monatsh Math 160, 337–341 (2010). https://doi.org/10.1007/s00605-008-0083-x

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  • DOI: https://doi.org/10.1007/s00605-008-0083-x

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