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
• DOI: 10.5565/publmat_362a92_24
• Títulos paralelos:
  • Comentarios sobre grupos nilpotentes casi finitamente generados
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• 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).