287 citations · 1.1k across the 26 of their papers we have counts for
6 papers · 1 filter
Revisiting Kneser's Theorem for Field Extensions
Christine Bachoc, Oriol Serra, Gilles Zémor
A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjectur…
An analogue of Vosper's Theorem for Extension Fields
Christine Bachoc, Oriol Serra, Gilles Zemor
We are interested in characterising pairs of -linear subspaces in a field extension such that the linear span of the set of products of elements of and of e…
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…
On the construction of dense lattices with a given automorphism group
Philippe Gaborit, Gilles Zemor
We consider the problem of constructing dense lattices of R^n with a given automorphism group. We exhibit a family of such lattices of density at least cn/2^n, which matches, up to…
On the critical pair theory in abelian groups : Beyond Chowla's Theorem
Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor
We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent resu…
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…