Profinite completions of some groups acting on trees
نویسنده
چکیده
We investigate the profinite completions of a certain family of groups acting on trees. It turns out that for some of the groups considered, the completions coincide with the closures of the groups in the full group of tree automorphisms. However, we introduce an infinite series of groups for which that is not so, and describe the kernels of natural homomorphisms of the profinite completions onto the aforementioned closures of respective groups.
منابع مشابه
Some remarks on profinite completion of spaces
We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of Artin-Mazur and Sullivan which extends also to non-connected spaces. Another new aspect is an equivariant profinite completion functor and equivariant fibrant replacement functor for a profinite group acting on a space. This is crucial for applications w...
متن کاملCartesian products as profinite completions
We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups under some natural restrictions.
متن کاملProfinite Heyting Algebras and Profinite Completions of Heyting Algebras
This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...
متن کاملProfinite Properties of Discrete Groups
This paper is based on a series of 4 lectures delivered at Groups St Andrews 2013. The main theme of the lectures was distinguishing finitely generated residually finite groups by their finite quotients. The purpose of this paper is to expand and develop the lectures. The paper is organized as follows. In §2 we collect some questions that motivated the lectures and this article, and in §3 discu...
متن کاملProfinite and pro-p completions of Poincaré duality groups of dimension 3
We establish some sufficient conditions for the profinite and prop completions of an abstract group G of type FPm (resp of finite cohomological dimension, of finite Euler characteristics) to be of type FPm over the field Fp for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristics). We apply our methods for orientable Poincaré duality groups G of ...
متن کامل