Conjugacy in special monoids (Q1178900)

By a special monoid we mean a monoid presented by a set of generators \(A\) and a set \(\{r_ i=e; i\in I\}\) of defining relations, where \(r_ i\) is a nonempty word over \(A\) and \(e\) is the empty word. In this paper the author investigates the problem of conjugacy in special monoids. He gives an affirmative answer to a problem proposed by \textit{F. Otto} [Semigroup Forum 29, 223-240 (1984; Zbl 0551.20044)]: The cyclic equality, left conjugacy and conjugacy are identical in a special monoid. Moreover, he proves that the conjugacy problem for a special monoid can be reduced to the conjugacy problem for the group of all its units, and the conjugacy problem is decidable for some restricted classes of special monoids.