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Gröbner-Shirshov bases and embedding of a semigroup in a group
E. G. Karpuz,A. S. Cevik,F. Ates,J. Koppitz 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.4
The main goal of this paper is to show that if a group G has a Gröbner-Shirshov basis that satisfies the condition R+, then the semigroup P having positive rules in < as a dening relation embeds in this group G. As a corollary of our result, we obtain that the semigroup B+ n+1 of braids can be embedded in the braid group. The main goal of this paper is to show that if a group G has a Grobner-Shirshov basis that satisfies the condition R+, then the semigroup P having positive rules in < as a dening relation embeds in this group G. As a corollary of our result, we obtain that the semigroup B+ n+1 of braids can be embedded in the braid group.