Decision problems concerning S-arithmetic groups

DOI10.2307/2274327zbMath0581.20045OpenAlexW2059620797MaRDI QIDQ3704085

Daniel Segal, Fritz J. Grunewald

Publication date: 1985

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2274327

zbMATH Keywords

algorithmsgeneratorslocalizationsreductive algebraic groupfundamental setsS-arithmetic groupseffective constructiontorsion-free finitely generated nilpotent groupsBruhat- Tits buildingfinitely generated \({\mathbb{Z}}(S)\)-moduleshomogeneous n-ary forms

Mathematics Subject Classification ID

Decidability and field theory (12L05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Classical groups (11E57) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (7)

Automorphisms of compact groups ⋮ Expansion in perfect groups. ⋮ Algorithms for arithmetic groups with the congruence subgroup property. ⋮ Towards a Pólya-Carlson dichotomy for algebraic dynamics ⋮ Linear groups and computation ⋮ Problems equivalent to rational Diophantine solvability ⋮ Commutators in $SL_2$ and Markoff surfaces I

Cites Work

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• Théoremes de finitude en cohomologie galoisienne
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• A Proof by Classical Methods of a Result of Axon Polynomial Congruences Modulo a Prime
• How to solve a quadratic equation in integers
• GALOIS COHOMOLOGY AND SOME QUESTIONS OF THE THEORY OF ALGORITHMS
• Diophantine Problems Over Local Fields I
• THE PROBLEM OF STRONG APPROXIMATION AND THE KNESER-TITS CONJECTURE FOR ALGEBRAIC GROUPS

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