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Subgroups of Bounded Abelian Groups

  • Roger Hunter
  • Fred Richman
  • Elbert Walker
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)

Abstract

Valuated groups are a topic of central interest in Abelian group theory. On one hand, they provide a viewpoint for classical Abelian theory problems, and on the other hand are of interest in their own right. In this latter regard, there has been some progress in getting structure theorems for certain valuated groups. Complete sets of invariants have been provided for finite direct sums of cyclic valuated p-groups [HRW1], for finite simply presented valuated p-groups (AHW), and for direct sums of torsion-free cyclic valuated groups [AHW]. A general discussion of simply presented valuated p-groups, with an aim toward a structure theory, is presented in [HW]. In [BHW], a basis for a general study of finite valuated p-groups is suggested. However, structure theories for simply presented valuated p-groups and for finite valuated p-groups are only in the initial stages.

Keywords

Abelian Group Cyclic Group Bounded Group Pure Subgroup Valuate Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [ALB]
    Albrecht, U. F., Valuated p-Groups and a Theorem of Szele, (preprint).Google Scholar
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    Arnold, D., R. Hunter, and E. Walker, Valuated Groups, Symposia Mathematica XXII(1979) 77–84.MathSciNetGoogle Scholar
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    Fuchs, L., Infinite Abelian Groups, New York, 1970.MATHGoogle Scholar
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    Hunter, R. and E. Walker, Valuated p-Groups, Leeiure Notes in Mathematics 874(1981) 350–373.CrossRefMathSciNetGoogle Scholar
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    Hunter, R., F. Richman and E. A. Walker, Finite direct sums of Cyclic Valuated p-Groups, Pacific. J. Math. 69(1977) 97–104.CrossRefMATHMathSciNetGoogle Scholar
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    Hunter, R. , F. Richman and E. A. Walker, Simply Presented Valuated Abelian p-Groups, J. Of Algebra, 49(1977) 125–133.CrossRefMATHMathSciNetGoogle Scholar
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    Richman, F., and E. A. Walker, Valuated Groups, J. Of Algebra, 56(1979) 145–167.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Roger Hunter
    • 1
  • Fred Richman
    • 1
  • Elbert Walker
    • 1
  1. 1.New Mexico State UniversityLas CrucesUSA

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