Israel Journal of Mathematics

, Volume 107, Issue 1, pp 1–16 | Cite as

On groups that are residually of finite rank



Letr be a fixed positive integer. A groupG has (Prüfer) rankr if every finitely generated subgroup ofG can be generated byr elements andr is the least such integer. In this paper we consider groups that are residually of rankr. Among other things we prove that a periodic group that is residually (of rankr and locally finite) is locally finite and obtain the structure of groups that are residually (of rankr and locally soluble). A number of examples are also given to illustrate the limitations of these theorems.


Normal Subgroup Finite Group Nilpotent Group Finite Index Finite Rank 
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Copyright information

© The Magnes Press 1998

Authors and Affiliations

  • Martyn R. Dixon
    • 1
  • Martin J. Evans
    • 1
  • Howard Smith
    • 2
  1. 1.Department of MathematicsUniversity of AlabamaTuscaloosaUSA
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA

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