Date of Degree
Algebra | Discrete Mathematics and Combinatorics | Geometry and Topology | Other Mathematics
Free Groups, Euclidean Buildings, Geometric Group Theory, Strong Schottky Lemma
We provide a criterion for two hyperbolic isometries of a Euclidean building to generate a free group of rank two. In particular, we extend the application of a Strong Schottky Lemma to buildings given by Alperin, Farb and Noskov. We then use this extension to obtain an infinite family of matrices that generate a free group of rank two. In doing so, we also introduce an algorithm that terminates in finite time if the lemma is applicable for pairs of certain kinds of matrices acting on the Euclidean building for the special linear group over certain discretely valued fields.
Ferguson, Michael E., "A Stronger Strong Schottky Lemma for Euclidean Buildings" (2023). CUNY Academic Works.
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