Abstract:
For soluble groups of finite rank we obtain the necessary and sufficient condition to be a virtually residually finite p-group. We also prove that a soluble group G of finite rank is residually π-finite for some finite set π of primes if and only if it has no subgroups of type Q and the torsion radical of G is a finite group.
Keywords:
soluble group of finite rank, virtually residually finite p-group.
Citation:
D. N. Azarov, “Approximability of soluble groups of finite rank by certain classes of finite groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 8, 18–29; Russian Math. (Iz. VUZ), 58:8 (2014), 15–23