Grobner-shirshov bases and embedding of a semigroup in a group

Abstract

The main goal of this paper is to show that if a group G has a Grobner-Shirshov basis R that satisfies the condition R+, then the semigroup P (with positive rules in R as a defining relation) embeds in this group G. As a consequence of our result, we obtain that the semigroup B+n+1 of braids can be embedded in the braid group.