Let G denote an arbitrary group. If X is a subset of G, we define its square X^2 by X^2 = {ab | a, b ∈ X}. This paper deals with the following type of problems. Let X be a finite subset of a group G. Determine the structure of X if the following inequality holds: |X^2| ≤ α|X| + β for some small α ≥ 1 and small |β|. Such problems are called inverse problems of small doubling type. We solve a general inverse problem of small doubling type in a monoid, which is a subset of the Baumslag–Solitar group BS(1, 2). Here the Baumslag-Solitar groups BS(m, n) are two-generated groups with one relation, which are defined as follows: BS(m, n) = , where m and n are integers.

A small doubling structure theorem in a Baumslag-Solitar group

LONGOBARDI, Patrizia;MAJ, Mercede;
2015

Abstract

Let G denote an arbitrary group. If X is a subset of G, we define its square X^2 by X^2 = {ab | a, b ∈ X}. This paper deals with the following type of problems. Let X be a finite subset of a group G. Determine the structure of X if the following inequality holds: |X^2| ≤ α|X| + β for some small α ≥ 1 and small |β|. Such problems are called inverse problems of small doubling type. We solve a general inverse problem of small doubling type in a monoid, which is a subset of the Baumslag–Solitar group BS(1, 2). Here the Baumslag-Solitar groups BS(m, n) are two-generated groups with one relation, which are defined as follows: BS(m, n) = , where m and n are integers.
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/11386/4651040
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 9
social impact