Some remarks on almost finitely generated nilpotent groups.

Hilton, Peter, and Militello, Robert. "Some remarks on almost finitely generated nilpotent groups.." Publicacions Matemàtiques 36.2A (1992): 655-662. <http://eudml.org/doc/41742>.

@article{Hilton1992,
abstract = {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).},
author = {Hilton, Peter, Militello, Robert},
journal = {Publicacions Matemàtiques},
keywords = {finitely generated nilpotent groups; -local groups; fg-like nilpotent groups; Serre class; fg nilpotent groups},
language = {eng},
number = {2A},
pages = {655-662},
title = {Some remarks on almost finitely generated nilpotent groups.},
url = {http://eudml.org/doc/41742},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Hilton, Peter
AU - Militello, Robert
TI - Some remarks on almost finitely generated nilpotent groups.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2A
SP - 655
EP - 662
AB - 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).
LA - eng
KW - finitely generated nilpotent groups; -local groups; fg-like nilpotent groups; Serre class; fg nilpotent groups
UR - http://eudml.org/doc/41742
ER -