Schur's theorem and its relation to the closure properties of the non-abelian tensor product

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'...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-04, Vol.150 (2), p.993-1002
Main Authors: Donadze, G., Ladra, M., Páez-Guillán, P.
Format: Article
Language:English
Subjects:
Mathematical analysis
Tensors
Theorems
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2018.150