Bounded generation of \(\mathrm{SL}_2\) over rings of \(S\)-integers with infinitely many units
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Publication:1755545
DOI10.2140/ant.2018.12.1949zbMath1448.11198arXiv1708.09262OpenAlexW3125222032WikidataQ128727206 ScholiaQ128727206MaRDI QIDQ1755545
Aleksander Morgan, Balasubramanian Sury, Andrei S. Rapinchuk
Publication date: 10 January 2019
Published in: Algebra \& Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.09262
Units and factorization (11R27) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Structure of modular groups and generalizations; arithmetic groups (11F06) Class field theory (11R37)
Related Items (13)
Width of SL(n,𝒪S,I) ⋮ Explicit strong boundedness for higher rank symplectic groups ⋮ Idempotent factorizations of singular 2 × 2 matrices over quadratic integer rings ⋮ First order rigidity of non-uniform higher rank arithmetic groups ⋮ Bounded reduction for Chevalley groups of types \(E_6\) and \(E_7\) ⋮ Idempotent chains and bounded generation of \(\mathrm{SL}_2\) ⋮ Elementary bounded generation for SLn${\rm SL}_n$ for global function fields and n⩾3$n\geqslant 3$ ⋮ Integral points on varieties defined by matrix factorization into elementary matrices ⋮ Bounded generation for congruence subgroups of Sp4(R) ⋮ Bounded generation and commutator width of Chevalley groups: function case ⋮ Strong boundedness of split Chevalley groups ⋮ Words have bounded width in ⋮ Non-virtually abelian anisotropic linear groups are not boundedly generated
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