Abstract
We study the semicentre of a group algebra K[G] where K is a field of characteristic zero and G is a polycyclic-by-finite group suchthat Δ(G) is torsion-free abelian. Several properties about the structure of this ring are proved, in particular as to when is the semicentre a UFD. Examples are constructed when this is not the case. We also prove necessary and sufficient conditions for every normal element of K[G] which belongs to K[Δ(G)] to be the product of a unit and a semi-invariant.
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