Subgroups of R. Thompson's group F that are isomorphic to F
نویسندگان
چکیده
منابع مشابه
Elementary 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 ...
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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...
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We give examples of non-amenable ICC groups Γ with the Haagerup property, weakly amenable with constant Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra P ⊂ L(Γ) generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group...
متن کاملOn subgroups of R. Thompson’s group F and other diagram groups
In this paper, we continue our study of the class of diagram groups. Simply speaking, a diagram is a labelled plane graph bounded by a pair of paths (the top path and the bottom path). To multiply two diagrams, one simply identifies the top path of one diagram with the bottom path of the other diagram, and removes pairs of “reducible” cells. Each diagram group is determined by an alphabet X, co...
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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 ...
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ژورنال
عنوان ژورنال: Groups – Complexity – Cryptology
سال: 2011
ISSN: 1867-1144,1869-6104
DOI: 10.1515/gcc.2011.009