On a vector space analogue of Kneser's theorem
In a previous paper the author et al. [J. Number Theory 97, No. 1, 1--9 (2002; Zbl 1034.11020)] extended Kneser's theorem on set addition in groups to vector spaces as follows. If \(E\subset K\) are fields such that the algebraic closure of \(E\) in \(K\) is separable over \(E\) and \(A,B\) are finite dimensional \(E\)-subspaces of \(K\), then \[ \dim_E \, AB \geq \dim_E \, A + \dim_E \, B -\dim_E \, H(AB), \] where \(H(AB)\) is the stabilizer of \(AB\). The author conjectures that the separability assumption can be omitted and proves this in the case when dimension of \(\dim_E \, A \leq 5\).
scientific article; zbMATH DE number 5190772