Maximal finite subgroups and minimal classes.

DOI10.4171/LEM/60-3/4-1zbMath1325.16014arXiv1304.2597MaRDI QIDQ2349106

Gabriele Nebe, Renaud Coulangeon

Publication date: 17 June 2015

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

Full work available at URL: https://arxiv.org/abs/1304.2597

zbMATH Keywords

numbers of conjugacy classeslatticesmaximal ordersVoronoi algorithmsimple algebrasmaximal finite subgroupsminimal classesunit groups of orders

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Computational aspects of associative rings (general theory) (16Z05) Units, groups of units (associative rings and algebras) (16U60) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Cohomology of arithmetic groups (11F75) Orders in separable algebras (16H10)

Related Items (3)

A classification of the automorphism groups of polarized abelian threefolds over finite fields ⋮ On a classification of the automorphism groups of polarized abelian surfaces over finite fields ⋮ Resolutions for unit groups of orders

Cites Work

• The integral homology of \(\mathrm{PSL}_2\) of imaginary quadratic integers with nontrivial class group
• On the integral homology of \(\text{PSL}_4(\mathbb Z)\) and other arithmetic groups
• Small-dimensional classifying spaces for arithmetic subgroups of general linear groups
• Cohomology of congruence subgroups of \(SL(n,Z)\)
• Dual Cones and the Voronoi Algorithm
• On maximal finite irreducible subgroups of 𝐺𝐿(𝑛,𝐙). I: The five and seven dimensional case. II: The six dimensional case
• Classification of quintic eutactic forms
• The homological torsion of PSL$_2$ of the imaginary quadratic integers
• Perfect lattices over imaginary quadratic number fields
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