| Title:
|
Finite groups with prime graphs of diameter $5$ (English) |
| Author:
|
Gorshkov, Ilya B. |
| Author:
|
Kukharev, Andrey V. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
307-312 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a prime graph of finite groups. In particular, we expect finite groups with prime graphs of maximal diameter. (English) |
| Keyword:
|
finite group |
| Keyword:
|
prime graph |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 1477.20046 |
| idMR:
|
MR4197082 |
| . |
| Date available:
|
2021-03-03T09:01:23Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148711 |
| . |
| Reference:
|
[1] Gruber, A., Keller, T.M., Lewis, M.L., Naughton, K., Strasser, B.: A characterization of the prime graphs of solvable groups.Journal of Algebra, 442, 2015, 397-422, Elsevier, MR 3395066, 10.1016/j.jalgebra.2014.08.040 |
| Reference:
|
[2] Kondrat'ev, A.S.: Prime graph components of finite simple groups.Matematicheskii Sbornik, 180, 6, 1989, 787-797, Russian Academy of Sciences, English transl. Math. USSR-Sb. 67 (1990), 235--247.. Zbl 0691.20013, MR 1015040 |
| Reference:
|
[3] Lucido, M.S.: The diameter of the prime graph of a finite group.Journal of Group Theory, 2, 2, 1999, 157-172, De Gruyter, MR 1681526 |
| Reference:
|
[4] Vasil'ev, A.V.: On connection between the structure of a finite group and the properties of its prime graph.Siberian Mathematical Journal, 46, 3, 2005, 396-404, Springer, 10.1007/s11202-005-0042-x |
| Reference:
|
[5] Vasil'ev, A.V.: On finite groups isospectral to simple classical groups.Journal of Algebra, 423, 2015, 318-374, Elsevier, MR 3283720, 10.1016/j.jalgebra.2014.10.013 |
| Reference:
|
[6] Williams, J.S.: The prime graph components of finite groups.Journal of Algebra, 69, 2, 1981, 487-513, MR 0617092, 10.1016/0021-8693(81)90218-0 |
| Reference:
|
[7] Yang, N., Grechkoseeva, M.A., Vasil'ev, A.V.: On the nilpotency of the solvable radical of a finite group isospectral to a simple group.Journal of Group Theory, 23, 3, 2020, 447-470, De Gruyter, MR 4092939 |
| . |
