This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab=c (mod n), with a, b, c being in the set. In a previous paper, we constructed an infinite sequence of integers (n(i))(i >= 1) and product-free sets S-i in Z/n(i)Z such that the density vertical bar S-i vertical bar/n(i) -> 1 as i -> infinity, where vertical bar S-i vertical bar denotes the cardinality of S-i. Here, we obtain matching, up to constants, upper and lower bounds on the maximal attainable density as n -> infinity.
2013. no 4, 827-845 p.