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Zbl 1197.11016
Hamidoune, Yahya Ould; Serra, Oriol; Zémor, Gilles
On some subgroup chains related to Kneser's theorem. (English)
[J] J. Théor. Nombres Bordx. 20, No. 1, 125-130 (2008). ISSN 1246-7405

{\it M. Kneser}'s theorem [Math. Z. 58, 459--484 (1953; Zbl 0051.28104); Math. Z. 61, 429--434 (1955; Zbl 0064.04305)] asserts that if $A$ and $B$ are subsets of an abelian group $G$, and $|AB|\leq |A|+|B|-2$, then there is a subgroup $H\subset G$ that depends on $A$ and $B$, so that $H\subset \text {stab}(AB)$. {\it É. Balandraud} [Ann. Inst. Fourier 58, No. 3, 915--943 (2008; Zbl 1143.11039)] proved a strengthening of Kneser's theorem in which the group $H$ depends only on the set $A$. In this paper, the authors prove a result about not-necessarily-abelian groups of which Balandraud's theorem is an easy consequence.
[Boris Bukh (Cambridge)]

MSC 2000:: *11B13 Additive bases
20E07 Subgroup theorems (group theory)

Keywords: Kneser's theorem; non-abelian groups; additive number theory

Citations: Zbl 1143.11039; Zbl 0051.28104; Zbl 0064.04305

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