PreprintCC BY-NC-ND 4.0arXiv
On Finite Groups with Element Order Set of Width 3
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)≤192 for every finite group G with α(G)≤3.
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BibTeX
@misc{min2026finite,
title = {{On Finite Groups with Element Order Set of Width 3}},
author = {Eric Min and Chloe So and Yong Yang and Eddy Zhang and Mengtian Zhang and Cody Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29004},
eprint = {2610.29004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29004},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On Finite Groups with Element Order Set of Width 3
AU - Eric Min
AU - Chloe So
AU - Yong Yang
AU - Eddy Zhang
AU - Mengtian Zhang
AU - Cody Zhou
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29004
UR - https://arxiv.org/abs/2610.29004
AB - 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)≤192 for every finite group G with α(G)≤3.
ER -