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1 results

  • Valuated Butler groups of finite rank

  • Part of
  • L. Fuchs, K. M. Rangaswamy
  • Journal:
    Journal of the Australian Mathematical Society / Volume 80 / Issue 3 / June 2006
    Published online by Cambridge University Press:
    09 April 2009, pp. 335-350
    Print publication:
    June 2006
    • Article
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  • Valuated Butler groups of finite rank are investigated. The valuated B2-groups are both epic images and pure subgroups of completely decomposable valuated groups of finite rank (Theorem 3.1). However, there are fundamental changes in the theory of Butler groups when valuations are involved. We introduce valuated B1-groups and show that they are valuated B2-groups. Surprisingly, valuated B2-groups of rank greater than 1 need not be valuated B1 -groups, unless they carry a special kind valuation, see Theorem 7.1. Theorem 6.5 gives a full characterization of valuated B1 -groups of finite rank, generalizing Bican's characterization of Butler groups.