Let G denote an arbitrary group. If S is a subset of G, then we write S^2={xy | x, y ∈ S}. A well-known problem in additive number theory is to find the precise structure of S in the case when S is a finite subset of G and |S^2| ≤ α |S|+ β with α(the doubling coefficient) and |β| small. Problems of this kind are called inverse problems of small doubling type. In this paper we e study an inverse problem of small doubling type. We investigate the structure of a finitely generated group G such that for any set S of generators of G of minimal order we have |S^2|≤ 3|S| − β , where β ∈ {1, 2, 3}.
"Groups with numerical restrictions on minimal generating sets"
Patrizia Longobardi;Mercede Maj
2020-01-01
Abstract
Let G denote an arbitrary group. If S is a subset of G, then we write S^2={xy | x, y ∈ S}. A well-known problem in additive number theory is to find the precise structure of S in the case when S is a finite subset of G and |S^2| ≤ α |S|+ β with α(the doubling coefficient) and |β| small. Problems of this kind are called inverse problems of small doubling type. In this paper we e study an inverse problem of small doubling type. We investigate the structure of a finitely generated group G such that for any set S of generators of G of minimal order we have |S^2|≤ 3|S| − β , where β ∈ {1, 2, 3}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
