منابع مشابه
Random subgroups of Thompson’s group F
We consider random subgroups of Thompson’s group F with respect to two natural stratifications of the set of all k generator subgroups of this group. We find that the isomorphism classes of subgroups which occur with positive density vary greatly between the two stratifications. We give the first known examples of persistent subgroups, whose isomorphism classes occur with positive density withi...
متن کاملCommensurations and Subgroups of Finite Index of Thompson’s Group F
Thompson’s groups have been extensively studied since their introduction by Thompson in the 1960s, despite the fact that Thompson’s account [7] appeared only in 1980. They have provided examples of infinite finitely presented simple groups, as well as some other interesting counterexamples in group theory (see for example, Brown and Geoghegan [3]). Cannon, Floyd and Parry [4] give an excellent ...
متن کاملQuasi - Isometrically Embedded Subgroups of Thompson ’ S Group F 3
The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The interesting properties of Thompson’s gr...
متن کاملElementary Amenable Subgroups of R. Thompson's Group F
This paper contributes to the study of the subgroups of Thompson’s group F by constructing a sequence of subgroups of increasing complexity. The group F is an interesting finitely presented group with a pleasant, faithful representation in the group PLo(I) of orientation preserving, piecewise linear, self homeomorphisms of the unit interval. Thus our subgroups also lie in PLo(I). The subgroups ...
متن کاملRandom Generation of Finitely Generated Subgroups of a Free Group
We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size n, according to the uniform distribution over size n ...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2010
ISSN: 1661-7207
DOI: 10.4171/ggd/76