English

Geometrical approach to the free sovable groups

Group Theory 2007-05-23 v2 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.math/0405008,
  title  = {Geometrical approach to the free sovable groups},
  author = {A. Vershik and S. Dobrynin},
  journal= {arXiv preprint arXiv:math/0405008},
  year   = {2007}
}

Comments

14 pages

R2 v1 2026-07-22T17:04:57.586Z