Schur's theorem and its relation to the closure properties of the non-abelian tensor product
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912853441642496 |
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| author | Donadze, Guram Ladra, Manuel Páez-Guillán, Pilar |
| author_facet | Donadze, Guram Ladra, Manuel Páez-Guillán, Pilar |
| contents | We show that the Schur multiplier of a Noetherian group need not be finitely generated. We prove that the non-abelian tensor product of a polycyclic (resp. polycyclic-by-finite) group and a Noetherian group, is a polycyclic (resp. polycyclic-by-finite) group. We also prove new versions of Schur's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schur's theorem and its relation to the closure properties of the non-abelian tensor product Donadze, Guram Ladra, Manuel Páez-Guillán, Pilar Group Theory 18G10, 18G50 We show that the Schur multiplier of a Noetherian group need not be finitely generated. We prove that the non-abelian tensor product of a polycyclic (resp. polycyclic-by-finite) group and a Noetherian group, is a polycyclic (resp. polycyclic-by-finite) group. We also prove new versions of Schur's theorem. |
| title | Schur's theorem and its relation to the closure properties of the non-abelian tensor product |
| topic | Group Theory 18G10, 18G50 |
| url | https://arxiv.org/abs/2601.19764 |