On Some Subgroup Chains Related to Kneser's Theorem

Details On Some Subgroup Chains Related to Kneser's Theorem On Some Subgroup Chains Related to Kneser's Theorem

2007-04-03

arxiv.org/abs/0704.0382v1

J. de Theorie des Nombres de Bordeaux, 20 (2008) 125--130

Mathematics

Number Theory

Scientific paper

A recent result of Balandraud shows that for every subset S of an abelian group G, there exists a non trivial subgroup H such that |TS| <= |T|+|S|-2 holds only if the stabilizer of TS contains H. Notice that Kneser's Theorem says only that the stabilizer of TS must be a non-zero subgroup. This strong form of Kneser's theorem follows from some nice properties of a certain poset investigated by Balandraud. We consider an analogous poset for nonabelian groups and, by using classical tools from Additive Number Theory, extend some of the above results. In particular we obtain short proofs of Balandraud's results in the abelian case.

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