English

Groupoids and the algebra of rewriting in group presentations

Group Theory 2019-01-15 v1

Abstract

Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a 22--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.

Keywords

Cite

@article{arxiv.1901.04348,
  title  = {Groupoids and the algebra of rewriting in group presentations},
  author = {N. D. Gilbert and E. A. McDougall},
  journal= {arXiv preprint arXiv:1901.04348},
  year   = {2019}
}

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15 pages