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A structure theorem for small sumsets in nonabelian groups

Author
Serra, O.; Zemor, G.
Type of activity
Journal article
Journal
European journal of combinatorics
Date of publication
2013-11
Volume
34
Number
8
First page
1436
Last page
1453
DOI
https://doi.org/10.1016/j.ejc.2013.05.026 Open in new window
Abstract
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 char...
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants