| Title:
|
Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup (English) |
| Author:
|
Shi, Jiangtao |
| Author:
|
Li, Na |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1229-1233 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group. We prove that if every self-centralizing subgroup of $G$ is nilpotent or subnormal or a TI-subgroup, then every subgroup of $G$ is nilpotent or subnormal. Moreover, $G$ has either a normal Sylow $p$-subgroup or a normal $p$-complement for each prime divisor $p$ of $|G|$. (English) |
| Keyword:
|
self-centralizing |
| Keyword:
|
nilpotent |
| Keyword:
|
TI-subgroup |
| Keyword:
|
subnormal |
| Keyword:
|
$p$-complement |
| MSC:
|
20D10 |
| idZBL:
|
Zbl 07442488 |
| idMR:
|
MR4339125 |
| DOI:
|
10.21136/CMJ.2021.0512-20 |
| . |
| Date available:
|
2021-11-08T16:07:59Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149252 |
| . |
| Reference:
|
[1] Robinson, D. J. S.: A Course in the Theory of Groups.Graduate Texts in Mathematics 80. Springer, New York (1996). Zbl 0836.20001, MR 1357169, 10.1007/978-1-4419-8594-1 |
| Reference:
|
[2] Shi, J.: Finite groups in which every non-abelian subgroup is a TI-subgroup or a subnormal subgroup.J. Algebra Appl. 18 (2019), Article ID 1950159, 4 pages. Zbl 07096474, MR 3977820, 10.1142/S0219498819501597 |
| Reference:
|
[3] Shi, J., Zhang, C.: Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup.Arch. Math. 101 (2013), 101-104. Zbl 1277.20021, MR 3089764, 10.1007/s00013-013-0545-9 |
| Reference:
|
[4] Shi, J., Zhang, C.: A note on TI-subgroups of a finite group.Algebra Colloq. 21 (2014), 343-346. Zbl 1291.20018, MR 3192353, 10.1142/S1005386714000297 |
| Reference:
|
[5] Sun, Y., Lu, J., Meng, W.: Finite groups whose non-abelian self-centralizing subgroups are TI-subgroups or subnormal subgroups.J. Algebra Appl. 20 (2021), Article ID 2150040, 5 pages. Zbl 07347720, MR 4242212, 10.1142/S0219498821500407 |
| . |
