Characterization of some alternating groups by order and largest element order
نویسندگان
1 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran
doi
10.22060/ajmc.2021.19507.1047چکیده
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.
