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Projective limits of nilpotent Hall groups

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Abstract

By analogy with the notion of a pronilpotent W-group, we define the notion of a pronilpotent 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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Authors and Affiliations

  1. Tbilisi State University, Tbilisi, Georgia

    A. D. Tavadze

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  1. A. D. Tavadze
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 49, Algebra and Geometry, 2007.

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Tavadze, A.D. Projective limits of nilpotent Hall groups. J Math Sci 155, 670–696 (2008). https://doi.org/10.1007/s10958-008-9237-6

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