Remarks on Azarov's work on soluble groups of finite rank (Q331852)

The author proves the following: For a finite extension \(G\) of a soluble group of finite abelian subgroup rank and some finite set \(\pi \) of primes the following statements are equivalent: (a) \(G\) is a finite extension of a residually finite \( \pi \)-group, (b) \(\tau (G)\) is finite and \(\zeta _1 (\mathrm{Fitt}(H))\) is \(\pi \)-reduced for some normal subgroup \(H\) of \(G\) of finite index, (c) \(G\) is a finite extension of a residually finite nilpotent \(\pi \)-group. The main result of the article referred to in the title [\textit{D. N. Azorov}, ``Some residual properties of soluble groups of finite rank'', Chebyshevskiĭ Sb. 15, No. 1, 7--18 (2014; \url{doi:10.1234/XXXX-XXXX-2014-1-7-18})] was on soluble groups of abelian total rank and its proof seemed longer.