Work

On Finite Groups with Element Order Set of Width 3

Year: 2026

Type: preprint

Abstract: We study finite groups in which every element order is divisible by at most three distinct primes. We determine the possible nonabelian composition factors, prove that a nonabelian simple group with this property has at most $15$ prime divisors in its order, and deduce that $ρ(G)\leq192$ for every finite group $G$ with $α(G)\leq3$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29004

Authors: Min, Eric, So, Chloe, Yang, Yong, Zhang, Eddy, Zhang, Mengtian, Zhou, Cody

Institution: Texas State University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223210287

Cites: 1

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Related to: 10