Zariski density and computing with \(S\)-integral groups

DOI10.1016/j.jalgebra.2023.02.024OpenAlexW4323306268MaRDI QIDQ2698475

Alexander Hulpke, Alla S. Detinko, Dane L. Flannery

Publication date: 24 April 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.06236

zbMATH Keywords

algorithmstrong approximationZariski densitylinear group\(S\)-integral\(S\)-arithmetic

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear algebraic groups over arbitrary fields (20G15) Other matrix groups over rings (20H25) Software, source code, etc. for problems pertaining to group theory (20-04)

Uses Software

• GAP
• kbmag

Cites Work

• Algorithms for arithmetic groups with the congruence subgroup property.
• Free subgroups of \(SL(n,Z),\) \(n>2\), generated by transvections
• Subgroup growth.
• Finitely generated profinitely dense free groups in higher rank semi-simple groups
• 2-generation of simple Lie algebras and free dense subgroups of algebraic groups
• The strong approximation theorem and computing with linear groups
• On Ihara's modular group
• Le problème des groupes de congruence pour \(SL_2\)
• Generators For All Principal Congruence Subgroups of SL(n, Z) with n ≥3
• Zariski density and computing in arithmetic groups
• Identifying congruence subgroups of the modular group
• Zariski Dense Surface Subgroups in SL(4, )
• Endliche Gruppen I
• Algorithms for Experimenting with Zariski Dense Subgroups
• Freeness and 𝑆-arithmeticity of rational Möbius groups
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