Automorphisms and endomorphisms of lacunary hyperbolic groups
Copyright policy )Automorphisms and endomorphisms of lacunary hyperbolic groups
In this article we study automorphisms and endomorphisms of lacunary hyperbolic groups. We prove that every lacunary hyperbolic group is Hopfian, answering a question by Henry Wilton. In addition, we show that if a lacunary hyperbolic group has the fixed point property for actions on \mathbf R -trees, then it is co-Hopfian and its outer automorphism group is locally finite. We also construct lacunary hyperbolic groups whose automorphism group is infinite, locally finite, and contains any locally finite group given in advance.
- Université de Rennes 1 France
- French National Centre for Scientific Research France
- Mathematics Research Institute of Rennes France
- L'Institut Agro France
- University of Rennes 2 France
Hopf property, co-Hopf property, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Cancellation theory of groups; application of van Kampen diagrams, 510, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, small cancellation theory, lacunary hyperbolic groups, action on \(\mathbf R\)-trees, Groups acting on trees, Automorphism groups of groups, Geometric group theory, automorphisms groups, Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Hopf property, co-Hopf property, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Cancellation theory of groups; application of van Kampen diagrams, 510, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, small cancellation theory, lacunary hyperbolic groups, action on \(\mathbf R\)-trees, Groups acting on trees, Automorphism groups of groups, Geometric group theory, automorphisms groups, Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
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