On almost finitely generated nilpotent groups

Peter Hilton and Robert Militello

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-6

Abstract:

A nilpotent group G is fgp if G p , 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 G p ≃ H p 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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:725276

DOI: 10.1155/S0161171296000749

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