Construction of p-groups of intermediate growth that have a continuum of quotient groups
type: Item
instance of: scholarly article
title: Construction of p-groups of intermediate growth that have a continuum of quotient groups
zbMATH Open document ID: 0573.20037
DOI: 10.1007/BF02071786
published in: Algebra and Logic
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187277
review text: The author has previously constructed a continuum of 2-generator finitely approximable 2-groups of intermediate growth [Izv. Akad. Nauk SSSR, Ser. Mat. 48, No.5, 939-983 (1984)], and a continuum of finitely approximable p-groups of intermediate growth [Mat. Sb., Nov. Ser. 126(168), No.2 194- 214 (1985; Zbl 0568.20033)] which contains a continuum of non-isomorphic groups. For all of these groups, each of their proper quotient groups is finite. Now the author constructs for each prime p a finitely approximable finitely generated p-group of intermediate growth that has a continuum of non-isomorphic approximable quotient groups.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 3914570
zbMATH Keywords: 2-generator finitely approximable 2-groups of intermediate growth
zbMATH Keywords: finitely approximable p-groups
zbMATH Keywords: proper quotient groups
zbMATH Keywords: finitely approximable finitely generated p-group
author: R. I. Grigorchuk
MaRDI profile type: Publication
cites work: Embedding Methods for Periodic Groups
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cites work: Q3867969
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description: scientific article; zbMATH DE number 3914570