%0 Journal Article
%T Recognition by degree prime-power graph and order of some characteristically simple group
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z
%A Bahri, Afsane
%A Khosravi, Behrooz
%A Baniasad Azad, Morteza
%D 2021
%\ 02/01/2021
%V 2
%N 1
%P 11-15
%! Recognition by degree prime-power graph and order of some characteristically simple group
%K Degree prime power graph
%K order
%K characteristically simple group
%K Characterization
%R 10.22060/ajmc.2020.18418.1033
%X In this paper, by the order of a group and triviality of $O_p(G)$ for some prime $p$, we give a new characterization for some characteristically simple groups. In fact, we prove that if pϵ{5, 17, 23, 37, 47, 73} and n≤p, where $n$ is a natural number, then $Gcong{{rm PSL}(2,p)}^{n}$ if and only if $ |G|=|{{rm PSL}(2,p)}|^{n}$ and $ O_p(G)=1$.}Recently in [Qin, Yan, Shum and Chen, Comm. Algebra, 2019], the degree prime-power graph of a finite group have been introduced and it is proved that the Mathieu groups are uniquely determined by their degree prime-power graphs and orders. As a consequence of our results, we show that ${rm PSL}(2,p)^n$, where pϵ{5,17,23,37,47,73} and n≤p are uniquely determined by their degree prime-power graphs and orders.
%U https://ajmc.aut.ac.ir/article_4122_da8bcf27302b7048c4d44272e8b6fb02.pdf