Symmetric Complete Sum-free Sets in Cyclic Groups

We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0,13], answering a question of Cameron, and that the number of those contained in the cyclic group of order n is exponential in n. For primes p, we provide a full characterization of the symmetric complete sum-free subsets of Zp of size at least (13−c)⋅p, where c>0 is a universal constant.