منابع مشابه
On Endomorphisms of torsion-Free hyperbolic Groups
Let H be a torsion-free δ-hyperbolic group with respect to a finite generating set S. Let g1, . . . , gn and g1∗, . . . , gn∗ be elements of H such that gr∗ is conjugate to gr for each r = 1, . . . , n. There is a uniform conjugator if and only if W (g1∗, . . . , gn∗) is conjugate to W (g1, . . . , gn) for every word W in n variables and length up to a computable constant depending only on δ, ♯...
متن کاملComments on Strongly Torsion-free Groups
In the present note, we discuss certain observations made by the author in February 2009 concerning strongly torsion-free profinite groups [cf. [Mzk2], Definition 1.1, (iii)]. These observations grew out of e-mail correspondences between the author, Akio Tamagawa, and Marco Boggi, as well as oral discussions between the author and Akio Tamagawa. Definition 1. Let G be a profinite group. (i) We ...
متن کاملOn groups and fields interpretable in torsion-free hyperbolic groups
We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela’s description of imaginaries in torsion-free hy...
متن کاملGaussian Groups Are Torsion Free
Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...
متن کاملThe Structure of Torsion Abelian Groups given by Presentations by Peter Crawley and Alfred W, Hales
If each of the elements in R involves only one generator in X, then G(X, R) is a direct sum of cyclic groups. On the other hand, if G is any abelian group, then GÇ=G(X, i?), where each element in R involves at most three generators in X; indeed this isomorphism results if we take X = G and R equal to the set of all elements in F o of the form x+y~ z, where z = x+y in G. Our purpose here is to i...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2005
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/hai004