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Hypercentral Groups and Rings

  • B. A. F. WehrfritzEmail author
Chapter
  • 605 Downloads
Part of the Algebra and Applications book series (AA, volume 10)

Abstract

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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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary, University of LondonLondonUK

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