Characterization of some alternating groups by order and largest element order | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 5، دوره 3، شماره 1، اردیبهشت 2022، صفحه 35-44 اصل مقاله (324.63 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.19507.1047 | ||
| نویسندگان | ||
| Ali Mahmoudifar* ؛ Ayoub Gharibkhajeh | ||
| Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Finite simple group؛ Prime graph؛ The largest element order؛ Alternating group | ||
| مراجع | ||
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