%0 Journal Article
%T Characterization of some alternating groups by order and largest element order
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Mahmoudifar, Ali
%A Gharibkhajeh, Ayoub
%D 2022
%\ 02/01/2022
%V 3
%N 1
%P 35-44
%! Characterization of some alternating groups by order and largest element order
%K Finite simple group
%K prime graph
%K the largest element order
%K alternating group
%R 10.22060/ajmc.2021.19507.1047
%X The prime graph (or Gruenberg-Kegel graph) of a finite group is a well-known graph. In this paper, first, we investigate the structure of the finite groups with a non-complete prime graph. Then as an application, we prove that every alternating group $A_n$, where $n\leq 31$ is determined by its order and its largest element order. Also, we show that $A_{32}$ is not characterizable by order and the largest element order.
%U https://ajmc.aut.ac.ir/article_4571_0eeffa99b6d5b70cfaaa4ff5169af4f5.pdf