Plünnecke and Kneser type theorems for dimension estimates

Cédric Lecouvey (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

Given a division ring K containing the field k in its center and A,B two finite subsets of K\{0}, we give some analogues of Plünnecke and Kneser theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the dimensions of the k-linear spans of A and B. These Plünnecke type estimates are then generalized to the case of associative algebras. We also obtain an analogue in the context of division rings of a theorem by Tao classifying the sets of small doubling in a group.

Mots clés: Division ring; Kneser's theorem; Plünnecke-Ruzsa's inequalities

Domaines: Combinatoire [math.CO]

Cédric Lecouvey. Plünnecke and Kneser type theorems for dimension estimates. 2011. ⟨hal-00618241v2⟩