| Title:
|
Finite groups whose character degree graphs coincide with their prime graphs (English) |
| Author:
|
Erkoç, Temha |
| Author:
|
Yilmaztürk, Utku |
| Author:
|
Güloğlu, İsmail Ş. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
647-656 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
finite groups |
| Keyword:
|
character degree graph |
| Keyword:
|
prime graph |
| MSC:
|
20C15 |
| idZBL:
|
Zbl 06986962 |
| idMR:
|
MR3851881 |
| DOI:
|
10.21136/CMJ.2018.0553-16 |
| . |
| Date available:
|
2018-08-09T13:10:08Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147358 |
| . |
| Reference:
|
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| Reference:
|
[2] Lewis, M. L.: Solvable groups whose degree graphs have two connected components.J. Group Theory 4 (2001), 255-275. Zbl 0998.20009, MR 1839998, 10.1515/jgth.2001.023 |
| Reference:
|
[3] Lewis, M. L., Meng, Q.: Square character degree graphs yield direct products.J. Algebra 349 (2012), 185-200. Zbl 1251.20011, MR 2853633, 10.1016/j.jalgebra.2011.09.016 |
| Reference:
|
[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. Zbl 1034.20010, MR 1994528, 10.1016/S0021-8693(03)00346-6 |
| Reference:
|
[5] Zuccari, C. P. Morresi: Character degree graphs with no complete vertices.J. Algebra 353 (2012), 22-30. Zbl 1256.20006, MR 2872434, 10.1016/j.jalgebra.2011.11.029 |
| Reference:
|
[6] White, D. L.: Degree graphs of simple linear and unitary groups.Commun. Algebra 34 (2006), 2907-2921. Zbl 1105.20007, MR 2250577, 10.1080/00927870600639419 |
| Reference:
|
[7] Williams, J. S.: Prime graph components of finite groups.J. Algebra 69 (1981), 487-513. Zbl 0471.20013, MR 0617092, 10.1016/0021-8693(81)90218-0 |
| . |
