ON THE CONJUGACY PROBLEM FOR ONE-RELATOR MONOIDS WITH ELEMENTS OF FINITE ORDER
Louxin Zhang · International Journal of Algebra and Computation · 1992
A one-relator monoid has nontrivial elements of finite order if and only if its presentation has the form (A; (PQ)mP=(PQ)nP), where PQ is a primitive word and m>n≥0. The (left-)conjugacy problem for such a monoid is shown to be reducible to the same problem for its left monoid. In particular, the (left-)conjugacy problem is decidable for the monoids M(A;(PQ)mP=(PQ)nP), where m+n≥2.