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The invariants of projective linear group actions

Published online by Cambridge University Press:  17 April 2009

Huah Chu ,
Ming-Chang Kang  and
Eng-Tjioe Tan
Huah Chu
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan, 10764, Republic of China
Ming-Chang Kang
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan, 10764, Republic of China
Eng-Tjioe Tan
Affiliation:
Department of Mathical Sciences, National Chengchi University, Mucha, Taipei, Taiwan, 11623, Republic of China
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Abstract

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Let Fq be the field with q elements and let G = PGLn(Fq) or PSLn(Fq) act on Fq(x1,…,xn−1), the rational function field of n − 1 variables. Then Fq(x1,…,xn−1)G is purely transcendental over Fq. In fact, a set of n − 1 generators of Fq(x1,…xn−1)G, over Fq is exhibited. The case n = 2 is treated by direct computation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 107 - 117
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Dickson, L.E., ‘A fundamental system of invariants of the general modular linear group with a solution of the form problem’, Trans. Amer. Math. Soc. 12 (1911), 75–98.Google Scholar
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[3]Wilkerson, C., ‘A primer on the Dickson invariants’, in Proc. of the Northwestern Homotopy Theory Conference 19: Contemp. Math., pp. 421–434 (Amer. Math. Soc., Providence, RI., 1983).CrossRefGoogle Scholar