Virtually splitting the map from Aut(G) to Out(G)

2013/01/18 by Mathieu Carette, Carette, Mathieu
Computer Science · Engineering · Mathematics · #20F55 #20F67 #Advanced Materials and Mechanics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Primary 20F28 #math.GR #msc:20E36 #msc:20F28 #msc:20F55 #msc:20F67 #secondary 20E36 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1301.4446

10 pages, 1 figure

arxiv created 2013/01/18 · openalex publication_date 2013/01/18 · arxiv updated 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an elementary criterion on a group G for the map from Aut(G) to Out(G) to split virtually. This criterion applies to many residually finite CAT(0) groups and hyperbolic groups, and in particular to all finitely generated Coxeter groups. As a consequence the outer automorphism group of any finitely generated Coxeter group is residually finite and virtually torsion-free.

Related

• On the residual finiteness of outer automorphisms of relatively hyperbolic groups
• Outer automorphism groups of right-angled Coxeter groups are either\n large or virtually abelian
• Automorphisms of Coxeter groups
• Isomorphism problem for finitely generated fully residually free groups
• Aut-invariant quasimorphisms on groups