Primitive elements in the free product of two finite cyclic groups (Q1913338)

In a two-generator non-cyclic group an element \(u\) is called primitive if there exists an element \(v\) such that \(u\) and \(v\) generate the whole group. Here, for the free product \(G = \langle s, t\); \(s^a = t^b = 1\rangle\), \(a, b \geq 2\), of two cyclic groups there is given a complete description of those \(u \in G\) which are primitive.