The profinite completion of accessible groups
نویسندگان
چکیده
We introduce a class \({\mathcal {A}}\) of finitely generated residually finite accessible groups with certain natural restriction on one-ended vertex in their JSJ-decompositions. prove that the profinite completion almost detects its JSJ-decomposition and compute genus free products {A}}\).
منابع مشابه
Cohomological properties of the profinite completion of Bianchi groups
We prove that the Bianchi groups, that is the groups PSL(2,O) where O is the ring of integers in an imaginary quadratic number field, are good. This is a property introduced by J.P. Serre which relates the cohomology groups of a group to those of its profinite completion. We also develop properties of goodness to be able to show that certain natural central extensions of Fuchsian groups are res...
متن کاملProfinite Groups
γ = c0 + c1p+ c2p + · · · = (. . . c3c2c1c0)p, with ci ∈ Z, 0 ≤ ci ≤ p− 1, called the digits of γ. This ring has a topology given by a restriction of the product topology—we will see this below. The ring Zp can be viewed as Z/pZ for an ‘infinitely high’ power n. This is a useful idea, for example, in the study of Diophantine equations: if such an equation has a solution in the integers, then it...
متن کاملCohomology of Profinite Groups
A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible...
متن کاملThe profinite completion of the integers, the p-adic integers, and Prüfer p-groups
By a topological ring we mean a ring X with a Hausdorff topology such that (x, y) 7→ x + y, x 7→ −x, (x, y) 7→ x · y are continuous. A morphism of topological rings is a continuous homomorphism of rings. An inverse system of topological rings is a family of topological rings Xi and a family of morphisms πi,j : Xi → Xj for i, j ∈ I with i ≥ j, such that when i ≥ j ≥ k, πi,k = πj,k ◦ πi,j . If Y ...
متن کاملCohomology of Profinite Groups
The aim of this thesis is to study profinite groups of type FPn. These are groups G which admit a projective resolution P of Ẑ as a ẐJGK-module such that P0, . . . , Pn are finitely generated, so this property can be studied using the tools of profinite group cohomology. In studying profinite groups it is often useful to consider their cohomology groups with profinite coefficients, but pre-exis...
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: Monatshefte für Mathematik
سال: 2022
ISSN: ['0026-9255', '1436-5081']
DOI: https://doi.org/10.1007/s00605-022-01789-9