| Title:
|
On some finite 2-groups in which the derived group has two generators (English) |
| Author:
|
Benjamin, Elliot |
| Author:
|
Snyder, Chip |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
71-100 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank 0 and whose commutator subgroup is generated by two elements, is metabelian. We also prove that the minimal order of any 2-group with nonabelian commutator subgroup of 2-rank 2 is $2^{12}$. (English) |
| Keyword:
|
2-group |
| Keyword:
|
metabelian |
| MSC:
|
20D15 |
| idZBL:
|
Zbl 07655756 |
| idMR:
|
MR4541090 |
| DOI:
|
10.21136/CMJ.2022.0415-21 |
| . |
| Date available:
|
2023-02-03T11:08:00Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151505 |
| . |
| Reference:
|
[1] Benjamin, E., Snyder, C.: Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4.Acta Arith. 177 (2017), 375-392. Zbl 1401.11143, MR 3630722, 10.4064/aa8485-9-2016 |
| Reference:
|
[2] Blackburn, N.: On prime-power groups in which the derived group has two generators.Proc. Camb. Philos. Soc. 53 (1957), 19-27. Zbl 0077.03202, MR 0081904, 10.1017/S0305004100031959 |
| Reference:
|
[3] Blackburn, N.: On prime-power groups with two generators.Proc. Camb. Philos. Soc. 54 (1958), 327-337. Zbl 0083.01902, MR 0102557, 10.1017/S0305004100033521 |
| Reference:
|
[4] Huppert, B.: Endliche Gruppen. I.Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134. Springer, Berlin (1967), German. Zbl 0217.07201, MR 0224703, 10.1007/978-3-642-64981-3 |
| . |
