The swap conjecture
type: Item
instance of: scholarly article
title: The swap conjecture
zbMATH Open document ID: 0790.20053
author: Raymond F. Tennant
author: Edward C. Turner
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: Examples abound of groups with many, even infinitely many, Nielsen classes of generating sets. The other way round, the authors are unaware of any group with more than one equivalence class with respect to ``swap equivalence'' (``the swap conjecture''), where an ``elementary swap'' changes one generating set to another by changing a single entry. In this paper, these notions are related to relation modules and ``the relation space groups''. The topological proofs of several known related results are given. The swap conjecture is verified for free groups, free abelian groups, surface groups, and for some concrete one-relator groups.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F38
zbMATH DE Number: 168045
zbMATH Keywords: Nielsen equivalence
zbMATH Keywords: swap equivalence
zbMATH Keywords: Nielsen classes
zbMATH Keywords: generating sets
zbMATH Keywords: relation modules
zbMATH Keywords: relation space groups
zbMATH Keywords: free groups
zbMATH Keywords: free abelian groups
zbMATH Keywords: surface groups
zbMATH Keywords: one-relator groups
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072713
OpenAlex ID: W2036424834
Wikidata QID: Q123259346
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DOI: 10.1216/RMJM/1181072713
description: scientific article; zbMATH DE number 168045