On residually finite graph products
type: Item
instance of: scholarly article
title: On residually finite graph products
zbMATH Open document ID: 0649.20027
DOI: 10.1016/0022-4049(87)90136-8
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: Baumslag (1963) gave a famous criterion, in terms of filtrations, for an amalgamated free product of two groups to be residually finite. The concept of the fundamental group of a graph of groups generalizes the idea of amalgamated free product, and sufficient conditions for such a ``graph product'' to be residually finite are given in this paper. While essentially simple, based on a ``filtration'' using families of subgroups of the vertex groups, the conditions are notationally too complex to outline here.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 4059687
zbMATH Keywords: filtrations
zbMATH Keywords: amalgamated free product
zbMATH Keywords: residually finite
zbMATH Keywords: fundamental group
zbMATH Keywords: graph of groups
zbMATH Keywords: graph product
author: M. Shirvani
reviewed by: D. J. McCaughan
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90136-8
OpenAlex ID: W2028441425
cites work: On the Residual Finiteness of Generalised Free Products of Nilpotent Groups
cites work: Residually finite hnn extensions
cites work: Q3341041
cites work: On residually finite HNN-extensions
description: scientific article; zbMATH DE number 4059687