Automorphisms of Generalized Thompson Groups

@article{Brin1998AutomorphismsOG,
  title={Automorphisms of Generalized Thompson Groups},
  author={Matthew G. Brin and F. Guzm{\'a}n},
  journal={Journal of Algebra},
  year={1998},
  volume={203},
  pages={285-348}
}
0.1. Results. We study the automorphisms of some generalizations of Thompson’s groups and their underlying structures. The automorphism groups of two of Thompson’s original groups were analyzed in [2] and were shown to be “small” and “unexotic.” Our results differ sharply from [2] in that we show that the automorphism groups of the generalizations are “large” and have “exotic” elements. The term exotic is from [1] and is explained later in this introduction. Richard J. Thompson introduced the… Expand
Metrics and embeddings of generalizations of Thompson’s group $F$
The distance from the origin in the word metric for generalizations F (p) of Thompson’s group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing theExpand
OF THOMPSON'S GROUP F
The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elementsExpand
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We solve the twisted conjugacy problem on Thompson’s group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut+(F) are orbit decidable provided a certainExpand
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The automorphism group of Thompson's group F: subgroups and metric properties.
We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead toExpand
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Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut.G/ such that for ’ 2 H the Reidemeister number R.’/ is infinite. This includes all finitelyExpand
THOMPSON'S GROUP IS DISTORTED IN THE THOMPSON-STEIN GROUPS
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A relationship between twisted conjugacy classes and the geometric invariants Ωn
A group G is said to have the property R∞ if every automorphism $${\varphi \in {\rm Aut}(G)}$$ has an infinite number of φ-twisted conjugacy classes. Recent work of Gonçalves and Kochloukova uses theExpand
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We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a naturalExpand
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We describe, through the use of Rubin's theorem, the automorphism groups of the Higman-Thompson groups $G_{n,r}$ as groups of specific homeomorphisms of Cantor spaces $\mathfrak{C}_{n,r}$. ThisExpand
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