Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2023-02-03T11:08:00Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151505 |
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| 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 |
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