Embeddings of partially commutative nilpotent groups

We present an algorithm determining the existence of an isomorphic embedding of one finitely generated partially commutative nilpotent group of class $2$ in another. It is shown how such embeddings can be constructed. We also describe an algorithm determining the existence of an embedding of a finitely generated partially commutative nilpotent group of arbitrary class $l$ with respect to a graph of nonzero radius in a free nilpotent group of class $l$.