Rewriting Systems and Embedding of monoids in groups

Details Rewriting Systems and Embedding of monoids in groups Rewriting Systems and Embedding of monoids in groups

2008-04-08

arxiv.org/abs/0804.1206v2

Groups Complex. Cryptol. 1 (2009), no. 1, 131-140

Mathematics

Group Theory

Scientific paper

10.1515/GCC.2009.131

In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system $\Re$ that satisfies the condition that each rule in $\Re$ with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from $\Re$ embeds in the group. As an example, we give a simple proof that right angled Artin monoids embed in the corresponding right angled Artin groups. This is a special case of the well-known result of Paris \cite{paris} that Artin monoids embed in their groups.

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