Resumen de Some remarks on almost finitely generated nilpotent groups

Peter Hilton , Robert Militello

• 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).