Abstract
In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we provide two new sets of generators for the field of definition in case of quasi-arithmetic hyperbolic Coxeter groups. This work is a concise version of chapters 4 and 5 of the author’s Ph.D. thesis Dotti (Groups of hyperbolic isometries and their commensurability. PhD thesis, Department of mathematics, University of Fribourg 2020).
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