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Geometrical approach to the free sovable groups

A. Vershik·S. Dobrynin
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Abstract

We give a topological interpretation of the free metabelian group, following the plan described in [Ver1,Ver2]. This interpretation is based on considering the Caley graph of a finitely generated group G as one-dimensional complex; its homology group with integer coefficients as G-space; and corresponding extension of the homology group determinated by the canonical cocycle. This gives a recursive approach to free solvable groups of any degree of solvability. For metabelian case we calculate second cohomology and describe all satellite groups.

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A. Vershik, S. Dobrynin. 2004-11-18. Geometrical approach to the free sovable groups. https://arxiv.org/abs/math/0405008

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