TY - JOUR
ID - 4571
TI - Characterization of some alternating groups by order and largest element order
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Mahmoudifar, Ali
AU - Gharibkhajeh, Ayoub
AD - Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran
Y1 - 2022
PY - 2022
VL - 3
IS - 1
SP - 35
EP - 44
KW - Finite simple group
KW - prime graph
KW - the largest element order
KW - alternating group
DO - 10.22060/ajmc.2021.19507.1047
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4571.html
L1 - https://ajmc.aut.ac.ir/article_4571_5f334a3e023d1ce38b1c2d0b3cfb6a75.pdf
ER -