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Displaying similar documents to “Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics”

The triangle groups

Muhammad A. Albar, Walid M. Al-Hamdan (1993)

Rendiconti del Seminario Matematico della Università di Padova

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A factorization of elements in PSL(2, F), where F = Q, R

Jan Ambrosiewicz (2000)

Discussiones Mathematicae - General Algebra and Applications

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Let G be a group and Kₙ = {g ∈ G: o(g) = n}. It is prowed: (i) if F = ℝ, n ≥ 4, then PSL(2,F) = Kₙ²; (ii) if F = ℚ,ℝ, n = ∞, then PSL(2,F) = Kₙ²; (iii) if F = ℝ, then PSL(2,F) = K₃³; (iv) if F = ℚ,ℝ, then PSL(2,F) = K₂³ ∪ E, E ∉ K₂³, where E denotes the unit matrix; (v) if F = ℚ, then PSL(2,F) ≠ K₃³.