Indicability, residual finiteness, and simple subquotients of groups acting on trees
نویسندگان
چکیده
منابع مشابه
Superstable groups acting on trees
We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...
متن کاملBounding the Residual Finiteness of Free Groups
We find a lower bound to the size of finite groups detecting a given word in the free group. More precisely we construct a word wn of length n in non-abelian free groups with the property that wn is the identity on all finite quotients of size ∼ n2/3 or less. This improves on a previous result of BouRabee and McReynolds quantifying the lower bound of the residual finiteness of free groups. A gr...
متن کاملOn the residual finiteness of outer automorphisms of hyperbolic groups
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.
متن کاملReflections on the residual finiteness of one-relator groups
Let G D ha; b; : : : j r D 1i be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, ..., the groups G.r;w/ D ha; b; : : : j rrw D r2i are not residually finite and have the same finite images as G. The existence of this family of one-relator groups which are not residually finite reinforces what is b...
متن کاملAmenability of Groups Acting on Trees
This note describes the first example of a group that is amenable, but cannot be obtained by subgroups, quotients, extensions and direct limits from the class of groups locally of subexponential growth. It has a balanced presentation ∆ = 〈b, t| [b, t]b, [[[b, t], b], b]〉. In the proof, I show that ∆ acts transitively on a 3-regular tree, and that Γ = 〈b, b −1 〉 stabilizes a vertex and acts by r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2018
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2018.22.4163