On the simple $K_5$-groups

	On the simple $K_5$-groups
AUT Journal of Mathematics and Computing
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 تیر 1404
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2025.23312.1249
نویسنده
Behnam Ebrahimzadeh^*
Department of Mathematics, Persian Gulf university, Boshehr, Iran
چکیده
After classification of finite simple groups, the researchers dissucced about groups characterization by property. Properties, such as element order, the set of elements with the same order, graphs,etc. In other words if $G$ be a finite group and $M$ be a property then we say the group $G$ is characterized by property $M$ if by isomorphic $G$ be a only group by property $M$. One of the methods, is group characterization by largest element order. In other wrds, we say the group $G$ is characterized by largest element order $k(G)$ and order of $G$ if there exists the group $H$, so that if $k(G)=k(H)$ and $\|G\|=\|H\|$, then $G\cong H$. In this paper, we prove that the simple $K_5$-groups $PSL(6,2)$ and $PSU(6,2)$ can be uniquely determined by their order and the largest order of elements.
کلیدواژه‌ها
The largest order of elements؛ Prime graph؛ Frobenius group؛ Projective special linear group؛ Projective special unitary group

آمار تعداد مشاهده مقاله: 31

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