A simple presentation of a group with unsolvable word problem
type: Item
instance of: scholarly article
title: A simple presentation of a group with unsolvable word problem
zbMATH Open document ID: 0571.20027
author: Donald J. Collins
published in: Illinois Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Drawing on work of \textit{G. S. Céjtin} [Tr. Mat. Inst. Steklova 52, 172- 189 (1958; Zbl 0087.253)] and \textit{V. V. Borisov} [Mat. Zametki 6, 521- 532 (1969; Zbl 0211.341)] this note gives a short explicit presentation of a group with unsolvable word problem. The presentation in question has 10 generators and the relations involve only 421 occurrences of the generators. Allowing just a few single digit exponents the whole presentation can be displayed in a dozen lines of print. The example in question is actually implicit in the work of Céjtin and Borisov and this paper does no more than make it quite explicit.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
zbMATH DE Number: 3910616
zbMATH Keywords: presentation
zbMATH Keywords: unsolvable word problem
zbMATH Keywords: generators
zbMATH Keywords: relations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3910616