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

Jan Ambrosiewicz

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

nstitute of Mathematics, Technical University of Białystok, 15-351 Białystok, ul. Wiejska 45A, Poland

Abstract

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.

Keywords

ENG

factorization of linear groups, linear groups, matrix representations of groups, sets of elements of the same order in groups

J. Ambrosiewicz, On the property W for the multiplicative group of the quaternions algebra, Studia Univ. Babes-Bolyai Math. 25 (1980), no. 2, 2-3.
J. Ambrosiewicz, The property W² for the multiplicative group of the quaternions field, Studia Univ. Babes-Bolyai Math. 29 (1984), 63-67.
J. Ambrosiewicz, On the square of sets of the group SL(3,F), PSL(3,F), Demonstratio Math. 18 (1985), 963-968.
J. Ambrosiewicz, On square of sets of linear groups, Rend. Sem. Mat. Univ. Padova 75 (1986), 253-256.
J. Ambrosiewicz, Powers of sets in linear group, Demonstratio Math. 23 (1990), 395-403.
J. Ambrosiewicz, Square of set of elements of order two in orthogonal groups, Publ. Math. Debrecen 41 (1992), 189-198.
J. Ambrosiewicz, If K is a real field then cn(PSL(2,K)) = 4, Demonstratio Math. 29 (1996), 783-785.
E.W. Ellers, Bireflectionality in classical groups, Canad. J. Math. 29 (1977), 1157-1162.
E.W. Ellers, R. Frank, and W. Nolte, Bireflectionality of the weak orthogonal and the weak sympletic groups, J. Algebra 88 (1984), 63-67.

Title

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

Affiliations

Abstract

Keywords

Bibliography