Another criterion for supersolvability of finite groups

2022/01/13 by Marius Tărnăuceanu, Tărnăuceanu, Marius
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.2201.04760

arxiv created 2022/01/13 · openalex publication_date 2022/01/13 · arxiv updated 2022/01/14 · 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. In this paper, we prove that if o(G)<(31)/(12) , then G is supersolvable. Moreover, we have o(G)=(31)/(12) if and only if G≅ A₄. We also classify finite groups G satisfying o(G)<(31)/(12) .

Related

• On the average order of a finite group
• On two problems about order sequences of finite groups
• A characterization of A₅ by its average order
• On the supersolvability of a finite group by the sum of subgroup orders
• An affirmative answer to the Jainkin-Zapirain's question