On two-generator subgroups in \(\mathrm{SL}_2(\mathbb{Z})\), \(\mathrm{SL}_2(\mathbb{Q})\), and \(\mathrm{SL}_2(\mathbb{R})\)

DOI10.1016/j.jalgebra.2017.01.036zbMath1406.20046arXiv1605.05226OpenAlexW2963260100MaRDI QIDQ515615

Anastasiia Chorna, Katherine Geller, Vladimir Shpilrain

Publication date: 16 March 2017

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

Full work available at URL: https://arxiv.org/abs/1605.05226

zbMATH Keywords

matrix groupssubgroup membership problem

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Other matrix groups over fields (20H20)

Related Items (9)

Average-case complexity of the Whitehead problem for free groups ⋮ Randomness and complexity in matrix groups ⋮ Freeness and 𝑆-arithmeticity of rational Möbius groups ⋮ A sequence of algebraic integer relation numbers which converges to 4 ⋮ Solving the membership problem for parabolic Möbius monoids ⋮ Homological representations of low genus mapping class groups ⋮ Subgroups of 𝑆𝐿₂(ℤ) characterized by certain continued fraction representations ⋮ On the membership problem for some subgroups of \(SL_2(\mathbf{Z})\) ⋮ Non-freeness of groups generated by two parabolic elements with small rational parameters

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• On Discrete Groups of Mobius Transformations
• Pell's Equation and Two Generator Free Möbius Groups
• Groups Generated by two Parabolic Linear Fractional Transformations

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