| Title:
|
On weakly-supplemented subgroups and the solvability of finite groups (English) |
| Author:
|
Zhou, Qiang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
331-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G=HK$. In this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of $G$ are obtained. (English) |
| Keyword:
|
weakly-supplemented subgroup |
| Keyword:
|
complemented subgroup |
| Keyword:
|
solvable group |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| idZBL:
|
Zbl 07088787 |
| idMR:
|
MR3959947 |
| DOI:
|
10.21136/CMJ.2018.0301-17 |
| . |
| Date available:
|
2019-05-24T08:54:53Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147727 |
| . |
| Reference:
|
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| Reference:
|
[2] Doerk, K., Hawkes, T.: Finite Soluble Groups.De Gruyter Expositions in Mathematics 4, de Gruyter, Berlin (1992). Zbl 0753.20001, MR 1169099, 10.1515/9783110870138 |
| Reference:
|
[3] Guralnick, R. M.: Subgroups of prime power index in a simple group.J. Algebra 81 (1983), 304-311. Zbl 0515.20011, MR 0700286, 10.1016/0021-8693(83)90190-4 |
| Reference:
|
[4] Hall, P.: A characteristic property of soluble groups.J. Lond. Math. Soc. 12 (1937), 198-200. Zbl 0016.39204, MR 1575073, 10.1112/jlms/s1-12.2.198 |
| Reference:
|
[5] Hall, P.: Complemented groups.J. London Math. Soc. 12 (1937), 201-204. Zbl 0016.39301, MR 1575074, 10.1112/jlms/s1-12.2.201 |
| Reference:
|
[6] Huppert, B.: Endliche Gruppen I.Springer, Berlin (1967), German. Zbl 0217.07201, MR 0224703, 10.1007/978-3-642-64981-3 |
| Reference:
|
[7] Kong, Q., Liu, Q.: The influence of weakly-supplemented subgroups on the structure of finite groups.Czech. Math. J. 64 (2014), 173-182. Zbl 1321.20021, MR 3247453, 10.1007/s10587-014-0092-y |
| . |
