Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424375 | European Journal of Combinatorics | 2013 | 18 Pages |
Abstract
Let G be an arbitrary finite group and let S and T be two subsets such that |S|â¥2, |T|â¥2, and |TS|â¤|T|+|S|â1â¤|G|â2. We show that if |S|â¤|G|â4|G|1/2 then either S is a geometric progression or there exists a non-trivial subgroup H such that either |HS|â¤|S|+|H|â1 or |SH|â¤|S|+|H|â1. This extends to the nonabelian case classical results for abelian groups. When we remove the hypothesis |S|â¤|G|â4|G|1/2 we show the existence of counterexamples to the above characterization whose structure is described precisely.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Oriol Serra, Gilles Zémor,