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A structure theorem for small sumsets in nonabelian groups

Autor
Serra, O.; Zemor, G.
Tipus d'activitat
Article en revista
Revista
European journal of combinatorics
Data de publicació
2013-11
Volum
34
Número
8
Pàgina inicial
1436
Pàgina final
1453
DOI
https://doi.org/10.1016/j.ejc.2013.05.026 Obrir en finestra nova
Resum
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...
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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