  We prove an arithmetic regularity lemma for stable subsets of finite abelian
groups, generalising our previous result for high-dimensional vector spaces
over finite fields of prime order. A qualitative version of this generalisation
was recently obtained by the first author in joint work with Conant and Pillay,
using model-theoretic techniques. In contrast, the approach in the present
paper is highly quantitative and relies on several key ingredients from
arithmetic combinatorics.
