| Title:
|
Notes on the average number of Sylow subgroups of finite groups (English) |
| Author:
|
Lu, Jiakuan |
| Author:
|
Meng, Wei |
| Author:
|
Moretó, Alexander |
| Author:
|
Wu, Kaisun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1129-1132 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than $\frac {29}{4}$ then $G$ is solvable or $G/F(G)\cong A_5$. This generalizes an earlier result by the third author. (English) |
| Keyword:
|
Fitting subgroup |
| Keyword:
|
Sylow subgroup |
| Keyword:
|
composition factor |
| MSC:
|
20D20 |
| idZBL:
|
Zbl 07442478 |
| idMR:
|
MR4339115 |
| DOI:
|
10.21136/CMJ.2021.0229-20 |
| . |
| Date available:
|
2021-11-08T16:03:05Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149242 |
| . |
| Reference:
|
[1] Group, GAP: GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra. Version 4.4.Available at http://www.gap-system.org (2005). |
| Reference:
|
[2] Guralnick, R. M., Robinson, G. R.: On the commuting probability in finite groups.J. Algebra 300 (2006), 509-528 addendum ibid 319 2008 1822. Zbl 1100.20045, MR 2228209, 10.1016/j.jalgebra.2005.09.044 |
| Reference:
|
[3] M. Hall, Jr.: On the number of Sylow subgroups in a finite group.J. Algebra 7 (1967), 363-371. Zbl 0178.02102, MR 0222159, 10.1016/0021-8693(67)90076-2 |
| Reference:
|
[4] Isaacs, I. M., Loukaki, M., Moretó, A.: The average degree of an irreducible character of a finite group.Isr. J. Math. 197 (2013), 55-67. Zbl 1290.20006, MR 3096606, 10.1007/s11856-013-0013-z |
| Reference:
|
[5] Moretó, A.: The average number of Sylow subgroups of a finite group.Math. Nachr. 287 (2014), 1183-1185. Zbl 1310.20026, MR 3231532, 10.1002/mana.201300064 |
| . |
