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The invariants of orthogonal group actions

Published online by Cambridge University Press:  17 April 2009

Li Chiang  and
Yu-Ching Hung
Li Chiang
Affiliation:
Department of Mathematics National, Taiwan Normal University, Taipei Taiwan, Republic of China
Yu-Ching Hung
Affiliation:
Department of Mathematics National, Taiwan Normal University, Taipei Taiwan, Republic of China
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Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on , O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 313 - 319
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Carlisle, D. and Kropholler, P.H., ‘Rational invariants of certain orthogonal and unitary groups’, (preprint).Google Scholar
[2]Chu, H., ‘Orthogonal group action on rational functions fields’, Bull. Inst. Math. Acad.Sinica 16 (1988), 115–122.Google Scholar
[3]Cohen, S.D., ‘Rational function invariant under an orthogonal group’, Bull. London Math.Soc. 22 (1990), 217–221.Google Scholar
[4]Jacobson, N., Basic algebra I, 1st ed. (Freeman and Company, New York, San Francisco, 1974).Google Scholar