Geodesic
Approximability of soluble groups of finite rank by certain classes of finite groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 18-29

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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 $\pi$-finite for some finite set $\pi$ 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. 
@article{IVM_2014_8_a1,
     author = {D. N. Azarov},
     title = {Approximability of soluble groups of finite rank by certain classes of finite groups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {18--29},
     publisher = {mathdoc},
     number = {8},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_8_a1/}
}
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D. N. Azarov. Approximability of soluble groups of finite rank by certain classes of finite groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 18-29. http://geodesic.mathdoc.fr/item/IVM_2014_8_a1/