On almost finitely generated nilpotent groups

A nilpotent group G is fgp if Gp, is finitely generated (fg) as a p-local group for all primes p; it is fg-like if there exists a nilpotent fg group H such that Gp≃Hp for all primes p. The fgp nilpotent groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelia...

Full description

Saved in:
Bibliographic Details
Main Authors: Peter Hilton, Robert Militello
Format: Article
Language:English
Published: Wiley 1996-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171296000749
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A nilpotent group G is fgp if Gp, is finitely generated (fg) as a p-local group for all primes p; it is fg-like if there exists a nilpotent fg group H such that Gp≃Hp for all primes p. The fgp nilpotent groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelian groups, a subgroup of an fg-like group is fg-like, and an extension of an fg-like group by an fg-like group is fg-like. These properties persist for nilpotent groups with finite commutator subgroup, but fail in general.
ISSN:0161-1712
1687-0425