Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru
Dear authors!
Submission of all materials is carried out only electronically through Online Submission System in
personal account.
DOI: 10.23671/VNC.2015.4.5967
Some residual properties of polycyclic groups and split extensions
Azarov D. N.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 4.
Abstract: It is proved that for every finite set \(\pi\) of primes there exists a polycyclic group which is a residually finite \(p\)-group if and only if the number \(p\) belongs to the set \(\pi\).
For citation: Azarov D. N. Some residual properties of polycyclic groups and split extensions. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol.17, no. 4, pp.3-10.
DOI 10.23671/VNC.2015.4.5967
1. Chandler B., Magnus V. Razvitie Kombinatornoj Teorii Grupp, M.,
Mir, 1985, 249 p. (Russian).
2. Mal'cev A. I. On isomorphic matrix representations of infinite
groups. Mat. Sbornik [Rec. Math. N.S.], 1940, vol. 8, pp. 405-422
(Russian).
3. Mal'cev A. I. Generalized nilpotent algebras and their associated
groups. Mat. Sbornik [Rec. Math. N.S.], 1949, vol. 25, pp. 347-366
(Russian).
4. Hirsh K. A. On infinite soluble groups. J. London Math. Soc.,
1952, vol. 27, pp. 81-85.
5. Shmel'kin A. L. Policiklicheskie gruppy. Sib. Mat. Zh. [Sib.
Math. J.], 1968, vol. 9, pp. 234-235 (Russian).
6. Gruenberg K. W. Residual properties of infinite soluble groups.
Proc. London Math. Soc., 1957, vol. 3(7), no. 25, pp. 29-62.
7. Azarov D. N. Approximability of finite rank soluble groups by
certain classes of finite groups. Russian Math. [Izv. Vyssh. Uchebn.
Zaved. Mat., 2014, vol. 58, no. 8, pp. 18-29], 2014, vol. 58, no. 8,
pp. 15-23.
8. Azarov D. N., Moldavanskij D. I. Approksimiruemost'
sverhrazreshimyh grupp konechnymi p-gruppami. Nauchn. Tr. Ivan. Gos.
Un-ta. Matematika, 1999, no. 2, pp. 8-9 (Russian).
9. Seksenbaev K. K teorii policiklicheskih grupp. Algebra i Logika
[Algebra and Logic], 1965, vol. 4, no. 3, pp. 79-83 (Russian).
10. Mal'cev A. I. O gomomorfizmah na konechnye gruppy. Uchen. Zap.
Ivan. Gos. Ped. In-ta, 1958, vol. 18, pp. 49-60 (Russian).
11. Azarov D. N. On the residual finiteness of p-groups.
Chebyshevskii Sb., 2010, vol. 11, no. 3, pp. 11-20 (Russian).
12. Aschenbrenner M., Friedl S. Residual properties of graph
manifold groups. Topology Appl., 2011, vol. 158 (10), pp. 1179-1191.
13. Kargapolov M. I., Merzljakov Ju. I. Osnovy Teorii Grupp, M.,
Nauka, 1972, 239 p. (Russian).