TY - JOUR
T1 - The invariants of orthogonal group actions
AU - Chiang, li
AU - Hung, yu Ching
PY - 1993/10
Y1 - 1993/10
N2 - Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]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.
AB - Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]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.
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U2 - 10.1017/S0004972700015720
DO - 10.1017/S0004972700015720
M3 - Article
AN - SCOPUS:84971744588
SN - 0004-9727
VL - 48
SP - 313
EP - 319
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 2
ER -