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Some remarks on almost finitely generated nilpotent groups

  • Autores: Peter Hilton, Robert Militello
  • Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 2, 1, 1992 (Ejemplar dedicado a: la memória de Pere Menal i Brufal), págs. 655-662
  • Idioma: inglés
  • Títulos paralelos:
    • Comentarios sobre grupos nilpotentes casi finitamente generados
  • Enlaces
  • Resumen
    • We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp @ Hp for all p. The we have proper set-inclusions:

      {fg} Ì {fg-like} Ì {fgp}.

      We examine the extent to which fg-like nilpotent groups satisfy the axioms for a Serre class. We obtain a complete answer only in the case that [G, G] is finite. (The collection of fgp nilpotent groups is known to form a Serre class in the extended sense).


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