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Abstract
Let K be a finitely generated field extension over Fp, and M be a finitely generated Fp[ϕ]-submodule of K with infinitely many elements, where ϕ is the p-Frobenius map. Under the assumption that there is some natural number n0 such that M∩Kpn0⊂ϕ(M), we fully characterize those positive-dimensional subgroups G of a split algebraic torus such that G(M) is equal to the ϕ-orbit of V(M) for some proper subvariety V of G.
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