Units of classical orders: A survey

zbMath0846.16027MaRDI QIDQ1909675

Ernst Kleinert

Publication date: 9 May 1996

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

zbMATH Keywords

virtual cohomological dimensionWhitehead groupsdivision algebrasarithmetic groupssemisimple algebrascongruence subgroup problemDirichlet's unit theoremindefinite quaternion orderslattice groups in skewfieldsunit groups of orders

Mathematics Subject Classification ID

Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Units, groups of units (associative rings and algebras) (16U60) Other algebras and orders, and their zeta and (L)-functions (11R54)

Related Items (18)

Presentations of the unit group of an order in a non-split quaternion algebra. ⋮ Unnamed Item ⋮ A dichotomy for integral group rings via higher modular groups as amalgamated products ⋮ Hyperbolic unit groups ⋮ Equivalence of Lattice Orbit Polytopes ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ Abelianization and fixed point properties of units in integral group rings ⋮ On global \(\mathcal{P}\)-forms ⋮ Computing zeta functions of table algebra orders using local zeta integrals ⋮ Geometric cycles, arithmetic groups and their cohomology ⋮ Group algebras of Kleinian type and groups of units. ⋮ From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups ⋮ Finite generation of units in alternative loop rings ⋮ Two theorems on units of orders ⋮ On the indecomposability of unit groups ⋮ Computing generators of free modules over orders in group algebras II ⋮ Structure of group rings and the group of units of integral group rings: an invitation ⋮ Computing in arithmetic groups with Voronoï's algorithm.

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