The prime graph (or Gruenberg-Kegel graph) of a finite group G is a familiar graph. In this paper first, we investigate the structure of the finite groups with a non-complete prime graph. Then we prove that every alternating group An, where n≤20 or n∈{23,24} is determined by its order and its largest element order.
@article{arxiv.2006.07961,
title = {Characterization of some alternating groups by order and the largest element order},
author = {Ali Mahmoudifar and Ayoub Gharibkhajeh},
journal= {arXiv preprint arXiv:2006.07961},
year = {2020}
}