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

Abstract

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.

9 pages

Cited by in corpus (1)

• Finiteness Conditions for the $n$-fold Tensor Product of Groups