Counting MSTD sets in finite abelian groups

In an abelian group G, a more sums than differences (MSTD) set is a subset A⊂G such that |A+A|>|A−A|. We provide asymptotics for the number of MSTD sets in finite abelian groups, extending previous results of Nathanson. The proof contains an application of a recently resolved conjecture of Alon and Kahn on the number of independent sets in a regular graph.