On a generalization of Shmel'kin's theorem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915891856277504 |
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| author | Mikheenko, Mikhail A. |
| author_facet | Mikheenko, Mikhail A. |
| contents | It is known that every nilpotent group contains solution of every finite unimodular system of equatiuons over itself. This statement, however, is not true for infinite systems. Moreover, there are abelian groups which disprove the infinite system analogue of the statement. It has already been researched which periodic abelian groups contain solutions of all infinite unimodular systems of equations over themselves. The present article covers the same question for periodic nilpotent groups and for torsion-free nilpotent groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25110 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a generalization of Shmel'kin's theorem Mikheenko, Mikhail A. Group Theory 20F70 (Primary), 20F18, 20F50, 11D88, 22A10 (Secondary) It is known that every nilpotent group contains solution of every finite unimodular system of equatiuons over itself. This statement, however, is not true for infinite systems. Moreover, there are abelian groups which disprove the infinite system analogue of the statement. It has already been researched which periodic abelian groups contain solutions of all infinite unimodular systems of equations over themselves. The present article covers the same question for periodic nilpotent groups and for torsion-free nilpotent groups. |
| title | On a generalization of Shmel'kin's theorem |
| topic | Group Theory 20F70 (Primary), 20F18, 20F50, 11D88, 22A10 (Secondary) |
| url | https://arxiv.org/abs/2603.25110 |