Residual finiteness of outer automorphism groups of certain tree products

2007 ◽  
Vol 10 (3) ◽  
Author(s):  
P. C Wong ◽  
K. B Wong
Keyword(s):  
Automorphism Groups ◽  
Outer Automorphism ◽  
Residual Finiteness ◽  
Outer Automorphism Groups

RESIDUAL FINITENESS OF OUTER AUTOMORPHISM GROUPS OF FINITELY GENERATED NON-TRIANGLE FUCHSIAN GROUPS

2005 ◽  
Vol 15 (01) ◽  
pp. 59-72 ◽  
Author(s):  
R. B. J. T. ALLENBY ◽  
GOANSU KIM ◽  
C. Y. TANG
Keyword(s):  
Automorphism Groups ◽  
Outer Automorphism ◽  
Fuchsian Groups ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Free Products ◽  
Residually Finite ◽  
Hnn Extensions ◽  
Outer Automorphism Groups ◽  
Orientable Surfaces

In [5] Grossman showed that outer automorphism groups of free groups and of fundamental groups of compact orientable surfaces are residually finite. In this paper we introduce the concept of "Property E" of groups and show that certain generalized free products and HNN extensions have this property. We deduce that the outer automorphism groups of finitely generated non-triangle Fuchsian groups are residually finite.

scholarly journals OUTER AUTOMORPHISM GROUPS OF CERTAIN TREE PRODUCTS OF ABELIAN GROUPS

2008 ◽  
Vol 77 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Y. D. CHAI ◽  
YOUNGGI CHOI ◽  
GOANSU KIM ◽  
C. Y. TANG
Keyword(s):  
Automorphism Groups ◽  
Abelian Groups ◽  
Outer Automorphism ◽  
Finitely Generated ◽  
Residually Finite ◽  
Outer Automorphism Groups

AbstractWe prove that certain tree products of finitely generated Abelian groups have Property E. Using this fact, we show that the outer automorphism groups of those tree products of Abelian groups and Brauner’s groups are residually finite.

scholarly journals Cannon–Thurston maps for $${{\,\mathrm{CAT}\,}}(0)$$ groups with isolated flats

2021 ◽  
Author(s):  
Beeker Benjamin ◽  
Matthew Cordes ◽  
Giles Gardam ◽  
Radhika Gupta ◽  
Emily Stark
Keyword(s):  
Automorphism Groups ◽  
Structure Theorem ◽  
Hyperbolic Group ◽  
Outer Automorphism ◽  
Hyperbolic Groups ◽  
Normal Subgroups ◽  
Infinite Index ◽  
Outer Automorphism Groups ◽  
Visual Boundaries

AbstractMahan Mitra (Mj) proved Cannon–Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group (Mitra in Topology, 37(3):527–538, 1998). We prove that Cannon–Thurston maps do not exist for infinite normal hyperbolic subgroups of non-hyperbolic $${{\,\mathrm{CAT}\,}}(0)$$ CAT ( 0 ) groups with isolated flats with respect to the visual boundaries. We also show Cannon–Thurston maps do not exist for infinite infinite-index normal $${{\,\mathrm{CAT}\,}}(0)$$ CAT ( 0 ) subgroups with isolated flats in non-hyperbolic $${{\,\mathrm{CAT}\,}}(0)$$ CAT ( 0 ) groups with isolated flats. We obtain a structure theorem for the normal subgroups in these settings and show that outer automorphism groups of hyperbolic groups have no purely atoroidal $$\mathbb {Z}^2$$ Z 2 subgroups.

Sign in / Sign up

Export Citation Format

Share Document