Free groups acting without fixed points on rational spheres

Kenzi Satô

Acta Arithmetica (1998)

  • Volume: 85, Issue: 2, page 135-140
  • ISSN: 0065-1036

Abstract

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For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.

How to cite

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Kenzi Satô. "Free groups acting without fixed points on rational spheres." Acta Arithmetica 85.2 (1998): 135-140. <http://eudml.org/doc/207158>.

@article{KenziSatô1998,
abstract = {For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.},
author = {Kenzi Satô},
journal = {Acta Arithmetica},
keywords = {rational special orthogonal groups; free groups of rotations},
language = {eng},
number = {2},
pages = {135-140},
title = {Free groups acting without fixed points on rational spheres},
url = {http://eudml.org/doc/207158},
volume = {85},
year = {1998},
}

TY - JOUR
AU - Kenzi Satô
TI - Free groups acting without fixed points on rational spheres
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 2
SP - 135
EP - 140
AB - For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.
LA - eng
KW - rational special orthogonal groups; free groups of rotations
UR - http://eudml.org/doc/207158
ER -

References

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  1. [C] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, New York, 1978. Zbl0395.10029
  2. [H] E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Akademische Verlagsgesellschaft, Leipzig, 1923. 
  3. [L] T. Y. Lam, Algebraic Theory of Quadratic Forms, W. A. Benjamin Inc., Massachusetts, 1973. Zbl0259.10019
  4. [M] L. J. Mordell, Diophantine Equations, Academic Press, New York, 1969. 
  5. [Sa0] K. Satô, A Hausdorff decomposition on a countable subset of 𝕊² without the Axiom of Choice, Math. Japon. 44 (1996), 307-312. Zbl0906.54009
  6. [Sa1] K. Satô, A free group acting without fixed points on the rational unit sphere, Fund. Math. 148 (1995), 63-69. Zbl0837.20034
  7. [Sa2] K. Satô, A free group of rotations with rational entries on the 3-dimensional unit sphere, Nihonkai Math. J. 8 (1997), 91-94. 
  8. [W] S. Wagon, The Banach-Tarski Paradox, Cambridge Univ. Press, Cambridge, 1985. Zbl0569.43001

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