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arXiv · 2610.29004

On Finite Groups with Element Order Set of Width 3

Eric Min·Chloe So·Yong Yang·Eddy Zhang·Mengtian Zhang·Cody Zhou
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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 $α(G)\leq3$.

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Eric Min, Chloe So, Yong Yang, Eddy Zhang, Mengtian Zhang, Cody Zhou. 2026-10-21. On Finite Groups with Element Order Set of Width 3. https://arxiv.org/abs/2610.29004

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