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math.NT2007
On Some Subgroup Chains Related to Kneser's Theorem
Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor
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…
math.NT2005
On the critical pair theory in Z/pZ
Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor
Let A and B be subsets of Z/pZ such that |A+B| < |A|+|B|+2. We prove that, if |A|>3, |B|>4, |A+B|<p-4 and p > 52, then A and B are included in arithmetic progressions with the same…