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2017
This chapter considers groups acting on trees. It examines which groups act on which spaces and, if a group does act on a space, what it says about the group. These spaces are called trees—that is, connected graphs without cycles. A group action on a tree is free if no nontrivial element of the group preserves any vertex or any edge of the tree.
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This chapter considers groups acting on trees. It examines which groups act on which spaces and, if a group does act on a space, what it says about the group. These spaces are called trees—that is, connected graphs without cycles. A group action on a tree is free if no nontrivial element of the group preserves any vertex or any edge of the tree.
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Rigidity of Branch Groups Acting on Rooted Trees
Geometriae Dedicata, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lavreniuk, Yaroslav +1 more
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1973
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/190476/2/7415688 ...
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PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/190476/2/7415688 ...
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On groups acting freely on a tree
Archiv der Mathematik, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Abstract Commensurators of Groups Acting on Rooted Trees
Geometriae Dedicata, 2002The author has previously constructed a family of finitely-presented, infinite, simple groups, each realized as the commutator subgroup of a group generated by a Higman-Thompson group and a group acting on a locally-finite, spherically-homogeneous tree. The current paper is motivated by the goal of obtaining a more algebraic description of these groups.
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Big free groups acting on $��$-trees
2014The set of homotopy classes of based paths in the Hawaiian earring has a natural $\mathbb R$-tree structure, but under that metric the action by the fundamental group is not by isometries. Following a suggestion by Cannon and Conner, this paper defines an $\mathbb R^ $-metric that does admit for an isometric action by the fundamental group.
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Acylindrical accessibility for groups acting on ?-trees
Mathematische Zeitschrift, 2004We prove an acylindrical accessibility theorem for finitely generated groups acting on ℝ-trees. Namely, we show that if G is a freely indecomposable non-cyclic k-generated group acting minimally and D-acylindrically on an ℝ-tree X then there is a finite subtree of measure at most 2D(k−1)+ɛ such that GT
Ilya Kapovich, Richard Weidmann
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Pro-p groups that act on profinite trees
Journal of Group Theory, 2008This paper is concerned with second countable pro-\(p\) groups that act on a profinite tree with trivial edge stabilizers. The motivation for this work lies in the fact that the structure of an abstract group acting on a tree can often be described in terms of the stabilizers and edges of the tree, using the Bass-Serre theory.
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Theory of groups that act on trees
Algebra and Logic, 1983The author gives a combinatorial proof of the well known theorem of Bass and \textit{J.-P. Serre} [Arbres, amalgams, \(SL_ 2\), Astérisque 46 (1977; Zbl 0369.20013)] on the structure of groups acting on trees. His proof is based on a theorem of \textit{A. M. Macbeath} [Ann. Math., II. Ser.
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