Finitely Presented Groups and Semigroups in Knot Theory

We construct finitely presented semigroups whose central elements are in one-to-one correspondence with the isotopy classes of non-oriented links in $\mathbb R^3$. Solving the word problem for those semigroups is equivalent to solving the classification problem for links and tangles. Also, we give a construction of finitely presented groups containing the braid group as a subgroup.