TY - JOUR
ID - 4122
TI - Recognition by degree prime-power graph and order of some characteristically simple group
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN -
AU - Bahri, Afsane
AU - Khosravi, Behrooz
AU - Baniasad Azad, Morteza
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 11
EP - 15
KW - Degree prime power graph
KW - order
KW - characteristically simple group
KW - Characterization
DO - 10.22060/ajmc.2020.18418.1033
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4122.html
L1 - https://ajmc.aut.ac.ir/article_4122_da8bcf27302b7048c4d44272e8b6fb02.pdf
ER -