Hypercentral Groups and Rings
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The theme of this chapter is the interplay between group-theoretic nilpotence properties of a group G and ring-theoretic nilpotence properties of its group ring Z G. Our main aim is to prove Roseblade’s theorems that Z G is a hypercentral ring if and only if G is a hypercentral group and that Z G is a polycentral ring if and only if G is a finitely generated nilpotent group. We must start by explaining these terms.
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