2023/07/28 by Ashkan Zarezadeh, Zarezadeh, Ashkan, Behrooz Khosravi +3
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.2307.15328
openalex publication_date 2023/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The average order of a finite group G is denoted by o(G). In this note, we classify groups whose average orders are less than o(S4), where S4 is the symmetric group on four elements. Moreover, we prove that G ≅ S4 if and only if o(G) = o(S4). As a consequence of our results we give a characterization for some finite groups by the average order. In [9, Theorem 1.2], the groups whose average orders are less than o(A4) are classified. It is worth mentioning that to get our results we avoid using the main theorems of [9] and our results leads to reprove those theorems.