# Some remarks on almost finitely generated nilpotent groups.

Peter Hilton; Robert Militello

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2A, page 655-662
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topHilton, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.