| Abstract | A theorem of Kneser in additive combinatorics states that in an abelian group G if A and B are finite subsets in G and AB={ab | a\in A, b\in B} then |AB|\geq |A|+|B|-|H(AB)|, where H(AB)={g | g\in G, g(AB)=AB}. More than a decade ago, motivated by the study of a problem about finite fields, we (jointly with Xiang-Dong Hou and Ka Hin Leung) proved an analogous result for vector spaces over a field E in an extension field K of E, which is now called a linear analogue of Kneser's theorem. This linear analogue has found some interesting applications and motivated further investigations. We will talk about this linear analogue of Kneser's theorem and related problems. |
