By analogy with the notion of a pronilpotent W-group, we define the notion of a pronilpo-tent Lie algebra and establish a one-to-one correspondence between pronilpotent W-groups and pronilpotent Lie algebras in the case where W is a field of zero characteristic; also, we establish a connection between free and projective groups of a given manifold. We prove that, for some manifolds, free and projective groups coincide; we investigate conditions under which a subgroup is free in an absolutely free pronilpotent W-group. In the class of pronilpotent groups, we introduce and discuss the notion of a free product; we construct an example which shows that an analog of the Kurosh theorem on subgroups of a free product does not hold even for finitely generated subgroups. A series of results stated in this paper was announced in [35-38].
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