A characterization of A₅ by its average order

2023/03/10 by Marius Tărnăuceanu, Tărnăuceanu, Marius
Engineering · Mathematics · Neuroscience · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Nuclear Receptors and Signaling #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2303.05881

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let o(G) be the average order of a finite group G. M. Herzog, P. Longobardi and M. Maj \cite7 showed that if G is non-solvable and o(G)=o(A₅), then G≅ A₅. In this note, we prove that the equality o(G)=o(A₅) does not hold for any finite solvable group G. Consequently, up to isomorphism, A₅ is determined by its average order.

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