G2-structures with torsion from half-integrable nilmanifolds

The equations for a G2-structure with torsion on a product M7=N6×S1 are studied in relation to the induced SU(3)-structure on N6. All solutions are found in the case when the Lee-form of the G2-structure is non-zero and N6 is a six-dimensional nilmanifold with half-integrable SU(3)-structure. Special properties of the torsion of these solutions are discussed.