TY - MGZN
AU - Serra, O.
AU - Zemor, G.
T2 - European journal of combinatorics
Y1 - 2013
VL - 34
IS - 8
SP - 1436
EP - 1453
DO - 10.1016/j.ejc.2013.05.026
AB - Let G be an arbitrary finite group and let S and T be two subsets such that |S| = 2, |T| = 2, and |T S| = |T| + |S| - 1 = |G| - 2. We show that if |S| = |G| - 4|G|1 / 2 then either S is a geometric progression or there exists a non-trivial subgroup H such that either |H S| = |S| + |H| - 1 or |S H| = |S| + |H| - 1. This extends to the nonabelian case classical results for abelian groups. When we remove the hypothesis |S| = |G| - 4|G|1 / 2 we show the existence of counterexamples to the above characterization whose structure is described precisely.
TI - A structure theorem for small sumsets in nonabelian groups
ER -