Free limits of Thompson’s group F

Akhmedov, Azer; Stein, Melanie; Taback, Jennifer

doi:10.1007/s10711-011-9583-2

Cited by 5 publications

(3 citation statements)

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“…(1) Non-elementary hyperbolic groups (see Akhmedov [4], with a refinement in by Olshansky and Sapir [48] on the number of generators of the free group); furthermore, [48,Remark 5] states, using results of Osin, that "strongly relatively hyperbolic groups" have infinite girth; (2) linear groups [4]; (3) one-relator groups [4]; (4) Thompson's group F (Brin shows in [17] that it preforms F 2 , and Akhmedov, Stein and Taback give a slightly worse estimate in [5]). …”

Section: Annales De L'institut Fouriermentioning

confidence: 99%

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Ordering the space of finitely generated groups

Bartholdi¹,

Erschler²

2015

Ann. inst. Fourier

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We consider the oriented graph whose vertices are isomorphism classes of finitely generated groups, with an edge from G to H if, for some generating set T in H and some sequence of generating sets S_i in G, the marked balls of radius i in (G,S_i) and in (H,T) coincide. Given a nilpotent group G, we characterize its connected component in this graph: if that connected component contains at least one torsion-free group, then it consists of those groups which generate the same variety of groups as G. The arrows in the graph define a preorder on the set of isomorphism classes of finitely generated groups. We show that a partial order can be imbedded in this preorder if and only if it is realizable by subsets of a countable set under inclusion. We show that every countable group imbeds in a group of non-uniform exponential growth. In particular, there exist groups of non-uniform exponential growth that are not residually of subexponential growth and do not admit a uniform imbedding into Hilbert space

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Section: Annales De L'institut Fouriermentioning

confidence: 99%

“…(4) Thompson's group F (Brin shows in [16] that it preforms F 2 , and Akhmedov, Stein and Taback give a slightly worse estimate [5]).…”

Section: Example 68 (Schleimer Olshansky and Sapir)mentioning

confidence: 99%

Ordering the space of finitely generated groups

Bartholdi¹,

Erschler²

2015

Ann. inst. Fourier

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show abstract

“…Recently Akhmedov, Stein and Taback [1] have proven that the free group on k generators is a limit of k-markings of Thompson's group F when k 3. The purpose of this paper is to prove the following.…”

Section: Introductionmentioning

confidence: 99%