Free groups acting without fixed points on rational spheres

• Autorzy: Kenzi Satô
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20E05: Free nonabelian groups
• 51F25: Orthogonal and unitary groups
• 51F20: Congruence and orthogonality
• 15A18: Eigenvalues, singular values, and eigenvectors
• 20H05: Unimodular groups, congruence subgroups
• 20H20: Other matrix groups over fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 2
• Strony: 135-140

Daty

wydano

1998

otrzymano

1997-01-21

poprawiono

1998-01-29

Twórcy

autor

Kenzi Satô

• Department of Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama 240, Japan

Bibliografia

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