On the residual finiteness of a class of polycyclic groups. II (Q6058436)

The authors investigate the residual finiteness of the polycyclic group \(A\rtimes \langle \phi \rangle\), where \(A\) is a free abelian group of rank \(n\) \((n\geq 2\)) and \(\phi\) is an automorphism of \(A\), and \(\phi\) is a cyclic permutation of the direct components twisted by a rational integer \(m\). They aim to figure out the finite index of the residually-finite-\(p\) normal subgroup in the given polycyclic group. For Part I see [the first author et al., Chin. Ann. Math., Ser. A 42, No. 1, 33--46 (2021; Zbl 1474.20066)].