Mathematical proceedings of the Cambridge Philosophical Society

Vol. 163, num. 3, p. 423-452

DOI: 10.1017/S0305004117000044

Date of publication: 2017-11-01

Abstract:

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.]]>