Download 3-manifold groups are virtually residually p by Matthias Aschenbrenner;Stefan Friedl PDF

By Matthias Aschenbrenner;Stefan Friedl

Given a major $p$, a bunch is termed residually $p$ if the intersection of its $p$-power index common subgroups is trivial. a gaggle is termed nearly residually $p$ if it has a finite index subgroup that is residually $p$. it really is famous that finitely generated linear teams over fields of attribute 0 are almost residually $p$ for all yet finitely many $p$. specifically, primary teams of hyperbolic $3$-manifolds are nearly residually $p$. it's also famous that basic teams of $3$-manifolds are residually finite. during this paper the authors turn out a typical generalisation of those effects: each $3$-manifold workforce is nearly residually $p$ for all yet finitely many $p$. this offers proof for the conjecture (Thurston) that basic teams of $3$-manifolds are linear teams

Show description

Read or Download 3-manifold groups are virtually residually p PDF

Similar nonfiction_13 books

The Later Philosophy of Wittgenstein

'David Pole, in his The Later Philosophy of Wittgenstein, makes an admirable try and make clear the crucial issues of Wittgenstein's philosophy in a simple demeanour. He methods it from the outdoor with sympathy and stable feel. and because he combines a transparent head with a fluent sort of writing – a mix that's infrequent one of the initiated – his publication will end up a superb creation if you want a succinct account of Wittgenstein's later philosophy with none mystical overtones.

The dialectics of liberation

A progressive compilation of speeches which produced a political foundation for lots of of the unconventional routine within the following many years The now mythical Dialectics of Liberation congress, held in London in 1967, used to be a distinct expression of the politics of dissent. Existential psychiatrists, Marxist intellectuals, anarchists, and political leaders met to debate key social matters.

Human Activity Recognition and Prediction

This publication offers a distinct view of human task acceptance, particularly fine-grained human job constitution studying, human-interaction attractiveness, RGB-D information established motion reputation, temporal decomposition, and causality studying in unconstrained human job video clips. The options mentioned provide readers instruments that offer an important development over current methodologies of video content material figuring out by means of making the most of task reputation.

Extra resources for 3-manifold groups are virtually residually p

Sample text

Writing Z = |Z| we note that Z = X. Clearly the finite index subgroup π1 (X ) of π1 (X ) = π1 (Xw ) forms a compatible collection of subgroups (of the graphs of groups associated to Z). Since we already showed that the conclusion of the proposition holds for graphs with one edge we now get a cover Z → Z = X which has the desired properties. A similar argument deals with the case that we have an edge e such that one component of Y \ {e} consists of a single vertex with no topological edge. Remarks.

Then X := Gn is central in G and Y := Hn is central in H, and both groups are elementary abelian p-groups; their fiber sum T over V := X ∩ U = Y ∩ U is an elementary abelian p-group, and X ∩ Y = V after identifying X and Y in the natural way with subgroups of T . By induction and after replacing G and H by compatible stretchings if necessary, we may assume that we have group morphisms θ : G → K and φ : H → K such that Ker(θ) = X, Ker(φ) = Y, θ|U = φ|U, and θ(G) ∩ φ(H) = θ(U ), as well as a central p-filtration K = {Ki } of K such that (1) Ki ∩ θ(G) = θ(Gi ) and Ki ∩ φ(H) = φ(Hi ) for 1 ≤ i ≤ n; (2) Ki ∩ θ(G) = θ(Gn ) and Ki ∩ φ(H) = φ(Hn ) for i ≥ n; (3) Li (G) ∩ Li (H) = Li (U ) (as subgroups of Li (K)) for 1 ≤ i < n, where U := G ∩ U = H ∩ U .

Suppose G is a p-group and char(R) = p. Then ω d = RG where d denotes the nilpotency class of ω. 2. Wreath products. 1. We recall the definition: Let X, H be groups. We turn the set X H of maps H → X into a group under the coordinate-wise operations. We have a right action H × X H → X H : (h, f ) → f h of H on X H , given by f h (k) = f (hk) for f ∈ X H and h, k ∈ H. The (unrestricted) wreath product of X and H is a semidirect product X H = H X H ; its underlying set is H × X H , with group operation (h1 , f1 ) · (h2 , f2 ) = (h1 h2 , f1h2 f2 ).

Download PDF sample

Rated 4.24 of 5 – based on 17 votes