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  • THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

  • Part of
  • YIN CHEN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 85 / Issue 1 / February 2012
    Published online by Cambridge University Press:
    18 August 2011, pp. 19-25
    Print publication:
    February 2012
    • Article
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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.