The solvability of a finite group by the sum of powers of element orders

2022/12/15 by Hiranya Kishore Dey, Dey, Hiranya Kishore
Computer Science · Mathematics · #20D60 #20E34 #20F16 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2212.07748

openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a new criterion for the solvability of the finite groups, depending on the function ψ_k(G) which is defined as the sum of k-th powers of the element orders of G. We show that our result can be used to show the solvability of some groups for which the solvability does not follow from earlier similar kind of results and we emphasize the following: looking at ψ_k(G) for k>1 can be useful to get further pieces of information about the group G.

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