Groupoids and the algebra of rewriting in group presentations

N. D. Gilbert, Emma A. McDougall

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Abstract

Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a 2-complex—the Squier complex—whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that key properties of the presentation are still encoded in the reduced form.
Original languageEnglish
Pages (from-to)623–639
Number of pages17
JournalBeiträge zur Algebra und Geometrie
Volume62
Early online date15 Sept 2020
DOIs
Publication statusPublished - Sept 2021

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