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A new characterization of some characteristically simple groups | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 11، دوره 4، شماره 1، 2023، صفحه 91-97 اصل مقاله (343.23 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21283.1083 | ||
| نویسنده | ||
| Zohreh Sayanjali* | ||
| Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Nonsolvable group؛ Prime-power graph | ||
| مراجع | ||
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[1] Z. Akhlaghi, M. Khatami, and B. Khosravi, Recognition of the simple groups PSL2(q) by character degree graph and order, Int. J. Group Theory, 8 (2019), pp. 41–46.
[2] H. Behravesh, M. Ghaffarzadeh, M. Ghasemi, and S. Hekmatara, Recognition of Janko groups and some simple K4-groups by the order and one irreducible character degree or character degree graph, Int. J. Group Theory, 10 (2021), pp. 1–10.
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[8] H. Xu, G. Chen, and Y. Yan, A new characterization of simple K3-groups by their orders and large degrees of their irreducible characters, Comm. Algebra, 42 (2014), pp. 5374–5380.
[9] R. Zhang and S. Liu, A characterization of linear groups L3(q) by their character degree graphs and orders, Bol. Soc. Mat. Mex. (3), 24 (2018), pp. 123–131. | ||
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