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On some subgroup chains related to Kneser’s theorem

Yahya Ould Hamidoune, Oriol Serra, Gilles Zémor (2008)

Journal de Théorie des Nombres de Bordeaux

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 | T S | | T | + | S | - 2 holds only if H S t a b ( T S ) . Notice that Kneser’s Theorem only gives { 1 } S t a b ( T S ) .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...

On sum-sets and product-sets of complex numbers

József Solymosi (2005)

Journal de Théorie des Nombres de Bordeaux

We give a simple argument that for any finite set of complex numbers A , the size of the the sum-set, A + A , or the product-set, A · A , is always large.

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