Let $G$ be a finite group and ${\rm cd}(G)$ 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: $10.22108/{\rm ijgt}.2019.113029.1502$.] 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.
Sayanjali, Z. (2023). A new characterization of some characteristically simple groups. AUT Journal of Mathematics and Computing, 4(1), 91-97. doi: 10.22060/ajmc.2022.21283.1083
MLA
Zohreh Sayanjali. "A new characterization of some characteristically simple groups". AUT Journal of Mathematics and Computing, 4, 1, 2023, 91-97. doi: 10.22060/ajmc.2022.21283.1083
HARVARD
Sayanjali, Z. (2023). 'A new characterization of some characteristically simple groups', AUT Journal of Mathematics and Computing, 4(1), pp. 91-97. doi: 10.22060/ajmc.2022.21283.1083
VANCOUVER
Sayanjali, Z. A new characterization of some characteristically simple groups. AUT Journal of Mathematics and Computing, 2023; 4(1): 91-97. doi: 10.22060/ajmc.2022.21283.1083