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Hafezieh, Roghayeh. (1397). On nonsolvable groups whose prime degree graphs have four vertices and one triangle. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7(3), 1-6. doi: 10.22108/ijgt.2017.21476
Roghayeh Hafezieh. "On nonsolvable groups whose prime degree graphs have four vertices and one triangle". سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7, 3, 1397, 1-6. doi: 10.22108/ijgt.2017.21476
Hafezieh, Roghayeh. (1397). 'On nonsolvable groups whose prime degree graphs have four vertices and one triangle', سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7(3), pp. 1-6. doi: 10.22108/ijgt.2017.21476
Hafezieh, Roghayeh. On nonsolvable groups whose prime degree graphs have four vertices and one triangle. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 1397; 7(3): 1-6. doi: 10.22108/ijgt.2017.21476

On nonsolvable groups whose prime degree graphs have four vertices and one triangle

International Journal of Group Theory
مقاله 2، دوره 7، شماره 3، آذر 2018، صفحه 1-6    اصل مقاله (185.17 K)
نوع مقاله: Ischia Group Theory 2016
شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21476
نویسنده
Roghayeh Hafezieh*
Department of‎ ‎Mathematics‎, ‎Gebze Technical University‎, ‎P.O.Box 41400, Gebze‎, ‎Turkey
چکیده
‎Let $G$ be a finite group‎. ‎The prime degree graph of $G$‎, ‎denoted‎ ‎by $\Delta(G)$‎, ‎is an undirected graph whose vertex set is $\rho(G)$ and there is an edge‎ ‎between two distinct primes $p$ and $q$ if and only if $pq$ divides some irreducible‎ ‎character degree of $G$‎. ‎In general‎, ‎it seems that the prime graphs‎ ‎contain many edges and thus they should have many triangles‎, ‎so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles‎. ‎In this paper we consider the case where for a nonsolvable group $G$‎, ‎$\Delta(G)$ is a connected graph which has only one triangle and four vertices‎.
کلیدواژه‌ها
prime degree graph؛ irreducible character degree؛ triangle
مراجع
[1] B. Huppert and W. Lempken, Simple groups of order divisible by at most four primes, Proc. of the F. Scorina Gomel State Univ., 16 (2000) 64–75.

[2] M. L. Lewis, An overview of graphs associated with character degrees and conjugacy class sizes in finite groups, Rocky Mountain J. Math., 38 (2008) 175–211.

[3] M. L. Lewis and D. L. White, Four-vertex degree graphs of nonsolvable groups, J. Algebra, 378 (2013) 1–11.

[4] H. P. Tong-Viet, Groups whose prime graphs have no triangles, Journal of Algebra, 378 (2013) 196–206.

[5] H. P. Tong-Viet, Prime graphs of finite groups with a small number of triangles, Monatsh. Math., 175 (2014) 457–484.

[6] D. L. White, Charcater degrees of extensions of PSL(2,q) and SL(2,q), J. Group Theory, 16 (2013) 1–33.

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