Orders of elements in finite quotients of Kleinian groups.

DOI10.2140/PJM.2012.256.211zbMATH Open1253.20052arXiv1104.0410OpenAlexW2963758501MaRDI QIDQ433544

Peter B. Shalen

Publication date: 5 July 2012

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Abstract: A positive integer $m$ will be called a {it finitistic order} for an element $gamma$ of a group $Gamma$ if there exist a finite group $G$ and a homomorphism $h:GammaoG$ such that $h(gamma)$ has order $m$ in $G$. It is shown that up to conjugacy, all but finitely many elements of a given finitely generated, torsion-free Kleinian group admit a given integer $m>2$ as a finitistic order.

Full work available at URL: https://arxiv.org/abs/1104.0410

zbMATH Keywords

finite quotientsunions of conjugacy classesfinitely generated Kleinian groupsfinitistic orders of elements

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) General geometric structures on low-dimensional manifolds (57M50) Residual properties and generalizations; residually finite groups (20E26) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

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