Abstract:
For soluble groups of finite rank we obtain the necessary and sufficient condition to be a virtually residually finite pp-group. We also prove that a soluble group GG of finite rank is residually ππ-finite for some finite set ππ of primes if and only if it has no subgroups of type QQ and the torsion radical of GG is a finite group.
Keywords:
soluble group of finite rank, virtually residually finite pp-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
\Bibitem{Aza14}
\by D.~N.~Azarov
\paper Approximability of soluble groups of finite rank by certain classes of finite groups
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 8
\pages 18--29
\mathnet{http://mi.mathnet.ru/ivm8915}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 8
\pages 15--23
\crossref{https://doi.org/10.3103/S1066369X14080027}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904637057}
Linking options:
https://www.mathnet.ru/eng/ivm8915
https://www.mathnet.ru/eng/ivm/y2014/i8/p18
This publication is cited in the following 6 articles:
D. N. Azarov, “O ππ-moschnosti niskhodyaschikh HNN-rasshirenii grupp”, Sib. matem. zhurn., 65:5 (2024), 775–784
D. N. Azarov, “Residually finite pp-groups of generalized free products of groups”, Russian Math. (Iz. VUZ), 61:5 (2017), 1–6
D. V. Goltsov, “Approksimiruemost fundamentalnoi gruppy konechnogo grafa grupp kornevym klassom grupp”, Chebyshevskii sb., 17:3 (2016), 64–71
D. N. Azarov, “Approksimatsionnye svoistva abelevykh grupp”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2015, no. 3(35), 5–11
D. N. Azarov, “Nekotorye approksimatsionnye svoistva politsiklicheskikh grupp i rasscheplyaemykh rasshirenii”, Vladikavk. matem. zhurn., 17:4 (2015), 3–10
D. I. Moldavanskii, “Kombinatornaya teoriya grupp v Ivanovskom gosudarstvennom universitete”, Chebyshevskii sb., 15:4 (2014), 32–54
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