Let $k$ be an algebraically closed field of characteristic 3. In this
paper we show that there are finitely many $GL(4,k)$-orbits in the
quotient of the module $ S^3 (k^4)$ of all cubic forms by the submodule
$ x^3 xS^1(k^4) of cubes of linear forms.
***To appear in the Journal of Algebra (Academic Press).
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