Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
finite groups; character degree graph; prime graph
finite groups; character degree graph; prime graph
Summary:
In the literature, there are several graphs related to a finite group $G$. Two of them are the character degree graph, denoted by $\Delta (G)$, and the prime graph, $\Gamma (G)$. In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.
References:
[1] Huppert, B.: Endliche Gruppen I. Die Grundlehren der Mathematischen Wissenschaften 134, Springer, Berlin (1967), German. DOI 10.1007/978-3-642-64981-3 | MR 0224703 | Zbl 0217.07201
[2] Lewis, M. L.: Solvable groups whose degree graphs have two connected components. J. Group Theory 4 (2001), 255-275. DOI 10.1515/jgth.2001.023 | MR 1839998 | Zbl 0998.20009
[3] Lewis, M. L., Meng, Q.: Square character degree graphs yield direct products. J. Algebra 349 (2012), 185-200. DOI 10.1016/j.jalgebra.2011.09.016 | MR 2853633 | Zbl 1251.20011
[4] Lewis, M. L., White, D. L.: Connectedness of degree graphs of nonsolvable groups. J. Algebra 266 (2003), 51-76 (2003) corrigendum ibid. 290 2005 594-598. DOI 10.1016/S0021-8693(03)00346-6 | MR 1994528 | Zbl 1034.20010
[5] Zuccari, C. P. Morresi: Character degree graphs with no complete vertices. J. Algebra 353 (2012), 22-30. DOI 10.1016/j.jalgebra.2011.11.029 | MR 2872434 | Zbl 1256.20006
[6] White, D. L.: Degree graphs of simple linear and unitary groups. Commun. Algebra 34 (2006), 2907-2921. DOI 10.1080/00927870600639419 | MR 2250577 | Zbl 1105.20007
[7] Williams, J. S.: Prime graph components of finite groups. J. Algebra 69 (1981), 487-513. DOI 10.1016/0021-8693(81)90218-0 | MR 0617092 | Zbl 0471.20013
Search
Partner of
