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} ⊂ {fg-like} ⊂ {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).
@article{urn:eudml:doc:41742,
title = {Some remarks on almost finitely generated nilpotent groups.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {655-662},
mrnumber = {MR1209830},
zbl = {0826.20032},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41742}
}
Hilton, Peter; Militello, Robert. Some remarks on almost finitely generated nilpotent groups.. Publicacions Matemàtiques, Tome 36 (1992) pp. 655-662. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41742/