A general small cancellation theory
type: Item
instance of: scholarly article
zbMATH Open document ID: 0980.20019
DOI: 10.1142/S0218196700000029
author: Jonathan P. McCammond
published in: International Journal of Algebra and Computation
publication date: 2001-11-19T00:00:00Z
Mathematics Subject Classification ID: 20F06
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 1570943
zbMATH Keywords: small cancellation theory
zbMATH Keywords: CW complexes
zbMATH Keywords: Cayley complexes
zbMATH Keywords: categories
zbMATH Keywords: van Kampen lemma
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: Dehn's algorithm
zbMATH Keywords: presentations
zbMATH Keywords: word problem
zbMATH Keywords: conjugacy problem
zbMATH Keywords: automorphism groups
MaRDI profile type: Publication
cites work: THE FREE BURNSIDE GROUPS OF SUFFICIENTLY LARGE EXPONENTS
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cites work: Fixed-point sets of group actions on finite acyclic complexes
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cites work: On torsion-free groups with infinitely many ends
title: A general small cancellation theory
review text: In this article a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. It is shown that many results about small cancellation groups are true also in this new setting.NEWLINENEWLINENEWLINEThe main results are summarized in Theorem A. If \(G=\langle A\mid R\rangle\) is a general small cancellation presentation with \(\alpha\leq 1/12\), then the word and conjugacy problems for \(G\) are decidable, the Cayley graph is constructible, the Cayley category of the presentation is contractible, and \(G\) is the direct limit of hyperbolic groups. If in addition, the presentation satisfies some additional hypotheses, then every finite subgroup of \(G\) is a subgroup of the automorphism group of some general relator in \(R\).
reviewed by: Vitaliĭ Roman'kov
description: scientific article