TY - JOUR
ID - 4864
TI - A new characterization of some characteristically simple groups
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Sayanjali, Zohreh
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Y1 - 2023
PY - 2023
VL - 4
IS - 1
SP - 91
EP - 97
KW - Nonsolvable group
KW - prime-power graph
DO - 10.22060/ajmc.2022.21283.1083
N2 - Let $G$ be a finite group and $\mathrm{cd}(G)$ be the set of irreducible complex character degrees of $G$. It was proved that some finite simple groups are uniquely determined by their orders and their degree graphs. Recently, in [Behravesh, et al., Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph, Int. J. Group Theory, DOI: 10.22108/ijgt.2019.113029.1502.] new characterizations for some finite simple groups are given. Also, in [Qin, et al., Mathieu groups and its degree prime-power graphs, Comm. Algebra, 2019] the degree prime-power graph of a finite group is introduced and it is proved that the Mathieu groups are uniquely determined by order and degree prime-power graph. In this paper we continue this work and we characterize some simple groups and some characteristically simple groups by their orders and some vertices of their degree prime-power graphs.
UR - https://ajmc.aut.ac.ir/article_4864.html
L1 - https://ajmc.aut.ac.ir/article_4864_c466f2fa6e86b0481f688edf99b8852a.pdf
ER -