Embedding of Free Nilpotent (Metabelian) Groups in Partially Commutative Nilpotent (Metabelian) Groups

An algorithm is presented that determines the maximum rank of a free nilpotent metabelian or, respectively, nilpotent group isomorphically embeddable into a given partially commutative nilpotent group of the same degree of nilpotency. It is shown how these embeddings are realized.