Metric Behaviour of the Magnus Embedding

2012/02/23 by Andrew W. Sale, Sale, Andrew W. · 1 citation
Mathematics · #20F16 #20F65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20F16 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1202.5343

9 pages. To appear in Geom. Dedicata. The final publication will be available at Springer via http://dx.doi.org/10.1007/s10711-014-9969-z

openalex publication_date 2012/02/23 · arxiv created 2014/02/17 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classic Magnus embedding is a very effective tool in the study of abelian extensions of a finitely generated group G, allowing us to see the extension as a subgroup of a wreath product of a free abelian group with G. In particular, the embedding has proved to be useful when studying free solvable groups. An equivalent geometric definition of the Magnus embedding is constructed and it is used to show that it is 2-bi-Lipschitz, with respect to an obvious choice of generating sets. This is then applied to obtain a non-zero lower bound on L_p compression exponents in free solvable groups.

Cited by

• The Geometry of the Conjugacy Problem in Wreath Products and Free Solvable Groups

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