JOURNAL OF GROUP THEORY, vol.20, no.2, pp.257-267, 2017 (SCI-Expanded)
We prove a conjecture of Boston that if p >= 5, all p-central quotients of the free group on two generators and of the free product of two cyclic groups of order p are Beauville groups. In the case of the free product, we also determine Beauville structures in p-central quotients when p = 3. As a consequence, we give an infinite family of Beauville 3-groups, which is different from the ones that were known up to date.