The conjugacy problem for centre-by-metabelian groups (Q1107628)

Noskov has recently proved that finitely presented groups in the variety of metabelian groups have solvable conjugacy problem. In this paper we look at the corresponding problem for centre-by-metabelian groups. We settle the conjugacy problem for certain relatively free centre-by- metabelian groups, including the free centre-by-metabelian groups of ranks 2 and 3.