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Archiv der Mathematik

, Volume 72, Issue 5, pp 321–327 | Cite as

Groups with all proper subgroups (finite rank)-by-nilpotent

  • Martyn R. Dixon
  • Martin J. Evans
  • Howard Smith

Abstract.

Let G be a group in which every proper subgroup is an extension of a group of finite (Prüfer) rank by a nilpotent group of class at most c. We show that if G is locally soluble-by-finite, then G is an extension of a group of finite rank by a nilpotent group of class at most c. This result is extended to cover groups G that belong to a certain extensive class \(\frak X \) of locally graded groups.

Keywords

Nilpotent Group Proper Subgroup Finite Rank Extensive Class 
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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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Martyn R. Dixon
    • 1
  • Martin J. Evans
    • 1
  • Howard Smith
    • 2
  1. 1.Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.US
  2. 2.Department of Mathematics, Bucknell University, Lewisburg, PA 17837, U.S.A.US

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