  A G-coloured knot is a knot together with a representation of its knot group
onto G. Two G-coloured knots are said to be rho-equivalent if they are related
by surgery around unit framed unknots in the kernels of their colourings. The
induced local move is a G-coloured analogue of the crossing change. For certain
families of metabelian groups G, we classify G-coloured knots up to
rho-equivalence. Our method involves passing to a problem about G-coloured
analogues of Seifert matrices.
