Some remarks on sets with small quotient set
  We prove, in particular, that for any finite set of real numbers A with |A/A| \ll |A| one has |A-A| > |A|^{5/3 - o(1)}. Also we show that |3A| > |A|^{2-o(1)} in the case. 
Ilya D. Shkredov
math.CO math.NT