Unimodular equations which do not preserve the derived length of a group
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916743656505344 |
|---|---|
| author | Mikheenko, Mikhail A. |
| author_facet | Mikheenko, Mikhail A. |
| contents | It is a known fact that any unimodular equation over an abelian group has a solution in that group itself. It is also known that for metabelian groups this does not hold; moreover, there is a unimodular equation over some metabelian group which has no solutions in any larger metabelian group. Here we present the proof of an analagous fact for solvable groups of higher derived lengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unimodular equations which do not preserve the derived length of a group Mikheenko, Mikhail A. Group Theory 20F70 (Primary), 20F16 (Secondary) It is a known fact that any unimodular equation over an abelian group has a solution in that group itself. It is also known that for metabelian groups this does not hold; moreover, there is a unimodular equation over some metabelian group which has no solutions in any larger metabelian group. Here we present the proof of an analagous fact for solvable groups of higher derived lengths. |
| title | Unimodular equations which do not preserve the derived length of a group |
| topic | Group Theory 20F70 (Primary), 20F16 (Secondary) |
| url | https://arxiv.org/abs/2505.12783 |