In this paper, we develop a new method to show that a monoid, given by a certain kind of presentation, embeds in a group. A mathematical device called the diamond condition was used in  to prove that the singular braid monoid SB_n embeds. Motivated by this, we consider monoid presentations which have the basic properties of the presentation of the singular braid monoid. In the same way as in , we prove that the monoid embeds. The proof of the diamond condition is completely geometric in , but here we prove it by using elementary algebraic properties.
Embedding, monoid presentation, group presentation, geometric braids.
KEYMAN, EBRU (2001) "A Class of Monoids Embeddable in a Group," Turkish Journal of Mathematics: Vol. 25: No. 2, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol25/iss2/5