Nilpotency of Loops

  • Richard Hubert Bruck
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE1, volume NF 20)

Abstract

Brück [70] contains a theory of nilpotency of loops which embodies some of the basic features of nilpotency for groups. We shall sketch a less general approach which seems conceptually simpler. Let 𝕷 be any class of loops such that:
  1. (a)

    Every subloop of a member of 𝕷 is in 𝕷.

     
  2. (b)

    Every loop which is a homomorphic image of a member of 𝕷 is in 𝕷.

     

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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Richard Hubert Bruck
    • 1
  1. 1.University of WisconsinMadisonUSA

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