If S is a subset of a group G, we define its square S^2 by the formula S^2 = {ab | a, b ∈S}. We prove that if S is a finite subset of an ordered group that generates a nonabelian group, then the order of S^2 is bigger or equal to 3|S|-2. This generalizes a classical result from the theory of set addition. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INDAM.
SMALL DOUBLING IN ORDERED GROUPS
LONGOBARDI, Patrizia;MAJ, Mercede
2014
Abstract
If S is a subset of a group G, we define its square S^2 by the formula S^2 = {ab | a, b ∈S}. We prove that if S is a finite subset of an ordered group that generates a nonabelian group, then the order of S^2 is bigger or equal to 3|S|-2. This generalizes a classical result from the theory of set addition. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INDAM.File in questo prodotto:
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