This article is cited in 7 papers

Approximability of soluble groups of finite rank by certain classes of finite groups

D. N. Azarov

Chair of Algebra and Mathematical Logic, Ivanovo State University, 37 Ermaka str., Ivanovo, 153025 Russia

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 $\pi$-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.

UDC: 512.543

Received: 01.02.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:8, 15–23

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