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For a prime p>2 and q=p^n, we compute a finite generating set for theSL_2(F_q)-invariants of the second symmetric power representation, showing theinvariants are a hypersurface and the field of fractions is a purelytranscendental extension of the coefficient field. As an intermediate result,we show the invariants of the Sylow p-subgroups are also hypersurfaces.

The invariants of the second symmetric power representation of SL_2(F_q)