Let \(({\mathcal A},{\mathcal H},F)\) be a \(p\)-summable Fredholm module where the algebra \({\mathcal A}= \mathbb{C}\Gamma\) is generated by a discrete group of unitaries in \({\mathcal L}({\mathcal H})\), which is of polynomial growth \(r\). Then the authors construct a spectral triple \(({\mathcal A},{\mathcal H},D)\) with \(F= \text{sign }D\) which is \(q\)-summable for each \(q> p+ r+1\). In the case when \(({\mathcal A},{\mathcal H},F)\) is \((p,\infty)\) summable they obtain \((q,\infty)\) summability of \(({\mathcal A},{\mathcal H},D)\) for each \(q> p+r+1\).