On the residual property of polycyclic groups
Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 121-126.

Voir la notice de l'article provenant de la source Math-Net.Ru

We generalize the result of A. L. Shmelkin which establishes the fact that polycyclic groups are virtually residually $p$-finite for any prime $p$.
Keywords: polycyclic group, residually a finite $p$-group, virtually residually a finite $p$-group.
@article{CHEB_2013_14_3_a14,
     author = {A. V. Rozov},
     title = {On the residual property of polycyclic groups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {121--126},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a14/}
}
TY  - JOUR
AU  - A. V. Rozov
TI  - On the residual property of polycyclic groups
JO  - Čebyševskij sbornik
PY  - 2013
SP  - 121
EP  - 126
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a14/
LA  - ru
ID  - CHEB_2013_14_3_a14
ER  - 
%0 Journal Article
%A A. V. Rozov
%T On the residual property of polycyclic groups
%J Čebyševskij sbornik
%D 2013
%P 121-126
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a14/
%G ru
%F CHEB_2013_14_3_a14
A. V. Rozov. On the residual property of polycyclic groups. Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 121-126. http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a14/

[1] Hirsh K. A., “On infinite soluble groups”, J. London Math. Soc., 27 (1952), 81–85 | DOI | MR

[2] Gruenberg K. W., “Residual properties of infinite soluble groups”, Proc. London Math. Soc., 7 (1957), 29–62 | DOI | MR | Zbl

[3] Azarov D. N., Moldavanskii D. I., “Approksimiruemost sverkhrazreshimykh grupp konechnymi $p$-gruppami”, Nauch. trudy IvGU. Matematika, 1999, no. 2, 8–9 | MR

[4] Shmelkin A. L., “Politsiklicheskie gruppy”, Sib. mat. zhurn., 9 (1968), 234–235 | MR

[5] Plotkin B. I., Gruppy avtomorfizmov algebraicheskikh sistem, Nauka, M., 1966 | MR | Zbl

[6] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[7] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1977 | MR | Zbl