@article{Guo2026, 
author = {Zheng Guo and Yong Hu and Cai-Heng Li},
title = {The Exceptional Hall Numbers},
year = {2026},
journal = {Peking Mathematical Journal},
volume = {9},
number = {3},
pages = {497-506},
keywords = {Hall subgroups, Hall numbers, Finite groups},
url = {https://www.sciopen.com/article/10.1007/s42543-025-00104-3},
doi = {10.1007/s42543-025-00104-3},
abstract = {A positive integer m is called a Hall number if any finite group of order precisely divisible by m has a Hall subgroup of order m. We prove that, except for the obvious examples, the three integers 12, 24 and 60 are the only Hall numbers, solving a problem proposed by Jiping Zhang.}
}