An analogue of Vosper's theorem for extension fields - BACHOC, CHRISTINE; SERRA, ORIOL; ZÉMOR, GILLES (Mathematical proceedings of the Cambridge Philosophical Society, 2017)
We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$ \dim_FST =\dim_F S+\dim_F T-1, $$\end{linenomath} when dim FS, dim FT ⩾ 2 and dim FST ⩽ [L : F] − 2.