Archiv der Mathematik

, Volume 71, Issue 5, pp 341–348 | Cite as

Radicals commuting with cartesian products

  • A.L.S. Corner
  • Rüdiger Göbel


For any radical R of abelian groups which does not commute with arbitrary cartesian products we define the norm \(\| R\| \) to be the least cardinal for which there exists a family, of this size, of groups \(G_\alpha \) such that \(R\prod G_\alpha \ne \prod R G_\alpha \). This norm \(\| R\| \) is always regular. Assuming GCH, we construct reduced products G to show that every regular cardinal \(\kappa \) which is not greater that any weakly compact cardinal is the norm of a suitable group radical RG.


Abelian Group Group Radical Arbitrary Cartesian Product Compact Cardinal Suitable Group 


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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • A.L.S. Corner
    • 1
  • Rüdiger Göbel
    • 2
  1. 1.Worcester College, Oxford, OX1 2HB, EnglandEngland
  2. 2.Fachbereich 6 Mathematik and Informatik, Universität Essen, D-45117 Essen, GermanyDeutschland

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