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 $nleq31$ 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.
Mahmoudifar, A., Gharibkhajeh, A. (2022). Characterization of some alternating groups by order and largest element order. AUT Journal of Mathematics and Computing, 3(1), 35-44. doi: 10.22060/ajmc.2021.19507.1047
MLA
Ali Mahmoudifar; Ayoub Gharibkhajeh. "Characterization of some alternating groups by order and largest element order". AUT Journal of Mathematics and Computing, 3, 1, 2022, 35-44. doi: 10.22060/ajmc.2021.19507.1047
HARVARD
Mahmoudifar, A., Gharibkhajeh, A. (2022). 'Characterization of some alternating groups by order and largest element order', AUT Journal of Mathematics and Computing, 3(1), pp. 35-44. doi: 10.22060/ajmc.2021.19507.1047
VANCOUVER
Mahmoudifar, A., Gharibkhajeh, A. Characterization of some alternating groups by order and largest element order. AUT Journal of Mathematics and Computing, 2022; 3(1): 35-44. doi: 10.22060/ajmc.2021.19507.1047
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