On the automorphism group of generalized Baumslag–Solitar groups

2005/11/03 by Gilbert Levitt · 1 citation
Computer Science · Mathematics · #Abelian group #Automorphism #Combinatorics #Finite Group Theory Research #Finitely-generated abelian group #Geometric and Algebraic Topology #Group (periodic table) #Mathematics #Nilpotent #Nilpotent group #Pure mathematics #Solvable group #Torsion (gastropod) #Unimodular matrix #Vertex (graph theory) #math.GR #math.GT #msc:20E08 #msc:20F65 #semigroups and automata theory

paper · pdf · doi:10.2140/gt.2007.11.473

published as Geom. Topol. 11 (2007) 473-515

arxiv created 2005/11/03 · openalex publication_date 2007/03/16 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out.G/ either contains non-abelian free groups or is virtually nilpotent of class 2. It has torsion only at finitely many primes.

Citations

• Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups
• On uniqueness of JSJ decompositions of finitely generated groups

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