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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
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.
MSC classification
Secondary:
12F20: Transcendental extensions
- Type
- Research Article
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- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2011
References
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