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Two-generated groups acting on trees
Archiv der Mathematik, 1999Let \(G\) be a group acting on a simplicial tree \(T\) without inversions, and let the edge stabilizers be non-trivial. If \(g,h\in G\) generate \(G\) (\(\langle g,h\rangle=G\)) or if \(\langle g,h\rangle\) is neither cyclic nor a free product of cyclic groups, then it is proved that the pair \(\{g,h\}\) is Nielsen equivalent to \(\{f,s\}\) and some ...
Kapovich, Ilya, Weidmann, Richard
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Groups acting freely on $��$-trees
2009A group is called $ $-free if it has a free Lyndon length function in an ordered abelian group $ $, which is equivalent to having a free isometric action on a $ $-tree. A group has a regular free length function in $ $ if and only if it has a free isometric action on a $ $-tree so that all branch points belong to the orbit of the base point.
Kharlampovich, O. +2 more
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Groups acting freely on R-trees
Ergodic Theory and Dynamical Systems, 1991AbstractIn this paper we study the question of which groups act freely on R-trees. The paper has two parts. The first part concerns groups which contain a non-cyclic, abelian subgroup. The following is the main result in this case.Let the finitely presented group G act freely on an R-tree.
John W. Morgan, Richard K. Skora
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The Nielsen Method For Groups Acting on Trees
Proceedings of the London Mathematical Society, 2002Geometric Nielsen methods are developed to study finitely generated subgroups of fundamental groups of graphs of groups. Ideas of H. Zieschang who applied Nielsen methods to free groups are generalized. When the group action is \(k\)-cylindrical, then the theory developed admits new results.
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1993
The exposition in this chapter is based on, and sometimes follows very closely, the book by Jean-Pierre Serre: Trees, Translated from the French by John Stillwell, Springer-Verlag, Berlin, Heidelberg, New York (1980). The reader should consult this work for more details, if needed.
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The exposition in this chapter is based on, and sometimes follows very closely, the book by Jean-Pierre Serre: Trees, Translated from the French by John Stillwell, Springer-Verlag, Berlin, Heidelberg, New York (1980). The reader should consult this work for more details, if needed.
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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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