Another criterion for supersolvability of finite groups

DOI10.1016/J.JALGEBRA.2022.04.017arXiv2201.04760MaRDI QIDQ6388138

Marius Tărnăuceanu

Publication date: 12 January 2022

Abstract: Let $o(G)$ be the average order of a finite group $G$. In this paper, we prove that if $o(G)<frac3112$,, then $G$ is supersolvable. Moreover, we have $o(G)=frac3112$ if and only if $Gcong{A}_4$. We also classify finite groups $G$ satisfying $o(G)<frac3112$,.

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

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