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

Jan Ambrosiewicz

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 159-167
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Jan Ambrosiewicz. "A factorization of elements in PSL(2, F), where F = Q, R." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 159-167. <http://eudml.org/doc/287631>.

@article{JanAmbrosiewicz2000,
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.},
author = {Jan Ambrosiewicz},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {factorization of linear groups; linear groups; matrix representations of groups; sets of elements of the same order in groups},
language = {eng},
number = {2},
pages = {159-167},
title = {A factorization of elements in PSL(2, F), where F = Q, R},
url = {http://eudml.org/doc/287631},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Jan Ambrosiewicz
TI - A factorization of elements in PSL(2, F), where F = Q, R
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 159
EP - 167
AB - 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.
LA - eng
KW - factorization of linear groups; linear groups; matrix representations of groups; sets of elements of the same order in groups
UR - http://eudml.org/doc/287631
ER -

References

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  1. [1] 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. Zbl0521.20017
  2. [2] J. Ambrosiewicz, The property W² for the multiplicative group of the quaternions field, Studia Univ. Babes-Bolyai Math. 29 (1984), 63-67. 
  3. [3] J. Ambrosiewicz, On the square of sets of the group SL(3,F), PSL(3,F), Demonstratio Math. 18 (1985), 963-968. Zbl0606.20037
  4. [4] J. Ambrosiewicz, On square of sets of linear groups, Rend. Sem. Mat. Univ. Padova 75 (1986), 253-256. 
  5. [5] J. Ambrosiewicz, Powers of sets in linear group, Demonstratio Math. 23 (1990), 395-403. 
  6. [6] J. Ambrosiewicz, Square of set of elements of order two in orthogonal groups, Publ. Math. Debrecen 41 (1992), 189-198. Zbl0812.20026
  7. [7] J. Ambrosiewicz, If K is a real field then cn(PSL(2,K)) = 4, Demonstratio Math. 29 (1996), 783-785. Zbl0874.20030
  8. [8] E.W. Ellers, Bireflectionality in classical groups, Canad. J. Math. 29 (1977), 1157-1162. Zbl0371.15009
  9. [9] E.W. Ellers, R. Frank, and W. Nolte, Bireflectionality of the weak orthogonal and the weak sympletic groups, J. Algebra 88 (1984), 63-67. Zbl0533.20020

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