Rational invariants of certain classical groups over finite fields |
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Authors: | Jizhu Nan Yin Chen |
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Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China |
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Abstract: | Let be a finite field with q elements, where q is a prime power. Let G be a subgroup of the general linear group over and be the rational function field over . We seek to understand the structure of the rational invariant subfield . In this paper, we prove that is rational (or, purely transcendental) by giving an explicit set of generators when G is the symplectic group. In particular, the set of generators we gave satisfies the Dickson property.
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Keywords: | Rational invariant Dickson invariant rational function field symplectic group |
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