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THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

Part of: Field extensions

Published online by Cambridge University Press:  18 August 2011

YIN CHEN
YIN CHEN*
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China (email: [email protected])
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Abstract

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Let Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

Keywords

invariants fieldfinite fieldprojective actions

MSC classification

Secondary: 12F20: Transcendental extensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 19 - 25
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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