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:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4386654
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
social impact