We answer a question raised by Lov\'asz and B. Szegedy [Contractors and
connectors in graph algebras, J. Graph Theory 60:1 (2009)] asking for a
contractor for the graph parameter counting the number of B-flows of a graph,
where B is a subset of a finite Abelian group closed under inverses. We prove
our main result using the duality between flows and tensions and finite Fourier
analysis. We exhibit several examples of contractors for B-flows, which are of
interest in relation to the family of B-flow conjectures formulated by Tutte,
Fulkerson, Jaeger, and others.Comment: 22 pages, 1 figur