The Magnus embedding is a quasi-isometry

2012/07/07 by Svetla Vassileva, Vassileva, Svetla
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1207.1830

7 pages

arxiv created 2012/07/07 · arxiv updated 2012/07/10

Abstract

We show that the Magnus embedding, which embeds the free solvable group of rank r and degree d into the wreath product of the free abelian group of rank r with the free solvable group of rank r and degree d-1, is a quasi-isometry.

Related

• Metric Behaviour of the Magnus Embedding
• The Magnus property for direct products
• Are free groups of different ranks bi-invariantly quasi-isometric?
• The kernel of the Magnus representation of the automorphism group of a free group is not finitely generated
• Free polynilpotent groups and the Magnus property