On a vector space analogue of Kneser's theorem
type: Item
instance of: scholarly article
title: On a vector space analogue of Kneser's theorem
zbMATH Open document ID: 1132.12003
author: Xiang-Dong Hou
published in: Linear Algebra and its Applications
publication date: 2007-09-13T00:00:00Z
review text: 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 \(\dim_E \, A \leq 5\).
reviewed by: Imre Z. Ruzsa
Mathematics Subject Classification ID: 12F15
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 11P70
zbMATH DE Number: 5190772
zbMATH Keywords: Kneser's theorem
zbMATH Keywords: separable extension
zbMATH Keywords: inseparable extension
zbMATH Keywords: vector space
MaRDI profile type: Publication
full work available at URL: j.laa.2007.04.019
OpenAlex ID: W1983095604
cites work: On the Addition of Residue Classes
cites work: New partial difference sets in \(\mathbb{Z}_{p^2}^t\) and a related problem about Galois rings
cites work: A generalization of an addition theorem of Kneser.
cites work: Abschätzung der asymptotischen Dichte von Summenmengen
cites work: Q4895030
DOI: 10.1016/J.LAA.2007.04.019
description: scientific article; zbMATH DE number 5190772