منابع مشابه
Homomorphisms between Diffeomorphism Groups
For r ≥ 3, p ≥ 2, we classify all actions of the groups Diffc(R) and Diff+(S) by Cdiffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of compactly supported diffeomorphisms on 1-manifolds. We show that all such actions have an elementary form, which we call topologically diagonal. As an application, we answer a question...
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THEOREM 1. Consider a split exact sequence of discrete groups Suppose there exists a normal series G = G 0 > G , o ... >(? " ^G n+1 = {1} (• •) such that: (1) GJG i+1 is a rational vector space for i = 0, ...,«; (2) GJG i+1 is contained in the centre ofG/G i+1 for i = 0,...,n; (3) there exists an element in the centre of T/G that induces a diagonalizable endomorphism of each GJG i+1 with all ei...
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Let k be an algebraically closed field of characteristic zero, L its finitely generated extension of transcendence degree ≥ 2, and L another finitely generated extension of k. It is a result of Bogomolov [B2] that any isomorphism between Gal(L/L) and Gal(L′/L) is induced by an isomorphism of fields L −→ L′ identifying L with L. If the transcendence degree of L over k is one, the group Gal(L/L) ...
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Definition: If (G, *) and (H, •) are groups, then a function f : G −→ H is a homomorphism if f (x * y) = f (x) • f (y) for all x, y ∈ G. Example: Let (G, *) be an arbitrary group and H = {e}, then the function f : G −→ H such that f (x) = e for any x ∈ G is a homomorphism. In fact, f (x * y) = e = e • e = f (x) • f (y).
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Given a graph X, define the presentation PX to have generators the vertices of X, and a relation xy = yx for each pair x, y of adjacent vertices. Let GX be the group with presentation PX, and given a field K, let KX denote the K"-algebra with presentation PX. Given graphs X and Y and a field K, it is known that the algebras KX and KY are isomorphic if and only if the graphs X and Y are isomorph...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1982
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700001486