The arithmetic structure of tetrahedral groups of hyperbolic isometries

DOI10.1112/S0025579300013097zbMath0668.20038MaRDI QIDQ3820810

Alan W. Reid, Colin Maclachlan

Publication date: 1989

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

quadratic formsgroups of unitsquaternion algebragroups generated by reflectionsFuchsian subgroupsarithmetic Kleinian groupcocompact Kleinian groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Discontinuous groups of transformations (57S30) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) General binary quadratic forms (11E16) Division rings and semisimple Artin rings (16Kxx)

Related Items

Mirror symmetries of hyperbolic tetrahedral manifolds ⋮ Commensurability classes of hyperbolic Coxeter groups. ⋮ Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ An embedding theorem for orders in central simple algebras ⋮ 3-manifolds from Platonic solids. ⋮ Fuchsian Subgroups of Bianchi Groups ⋮ Surface subgroups of Coxeter and Artin groups. ⋮ Arithmeticity, discreteness and volume ⋮ \(k\)-hypermonogenic automorphic forms ⋮ Optimal embeddings in quaternion algebras ⋮ Bianchi groups are conjugacy separable. ⋮ Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants ⋮ Dynamics of twisted Alexander invariants ⋮ On the graded quotients of the rings of Fricke characters of free groups. ⋮ Infinitely many arithmetic hyperbolic rational homology 3–spheres that bound geometrically

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