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.
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Original Russian Text © D.N. Azarov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 8, pp. 18–29.
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Azarov, D.N. Approximability of finite rank soluble groups by certain classes of finite groups. Russ Math. 58, 15–23 (2014). https://doi.org/10.3103/S1066369X14080027
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DOI: https://doi.org/10.3103/S1066369X14080027