Geodesic
Residual finiteness with respect to conjugacy of free polynilpotent groups
Sbornik. Mathematics, Tome 50 (1985) no. 2, pp. 299-323 
Yu. A. Kolmakov. Residual finiteness with respect to conjugacy of free polynilpotent groups. Sbornik. Mathematics, Tome 50 (1985) no. 2, pp. 299-323. http://geodesic.mathdoc.fr/item/SM_1985_50_2_a1/
@article{SM_1985_50_2_a1,
     author = {Yu. A. Kolmakov},
     title = {Residual finiteness with respect to conjugacy of free polynilpotent groups},
     journal = {Sbornik. Mathematics},
     pages = {299--323},
     year = {1985},
     volume = {50},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_50_2_a1/}
}
TY  - JOUR
AU  - Yu. A. Kolmakov
TI  - Residual finiteness with respect to conjugacy of free polynilpotent groups
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 299
EP  - 323
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1985_50_2_a1/
LA  - en
ID  - SM_1985_50_2_a1
ER  - 
%0 Journal Article
%A Yu. A. Kolmakov
%T Residual finiteness with respect to conjugacy of free polynilpotent groups
%J Sbornik. Mathematics
%D 1985
%P 299-323
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1985_50_2_a1/
%G en
%F SM_1985_50_2_a1

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

In this paper conditions are obtained for the residual finiteness with respect to conjugacy of groups of the form $F/R_k$, where $F$ is a free group, $R\triangleleft F$, and $R_k$ is the $k$th term of the lower central series of $R$. It is shown that free polynilpotent groups are residually finite with respect to conjugacy. The proof utilizes an embedding of groups of the form $F/R_k$ into a twisted wreath product of simpler groups. Properties of this embedding are also studied. Bibliography: 12 titles.

[1] Sarkisyan R. A., “Sopryazhennost v svobodnykh polinilpotentnykh gruppakh”, Algebra i logika, 11:6 (1972), 694–710

[2] Remeslennikov V. N., Sokolov V. G., “Nekotorye svoistva vlozheniya Magnusa”, Algebra i logika, 9:5 (1970), 566–578 | MR | Zbl

[3] Malkhasyan A. Sh., Mamuchishvili A. I., “O finitnoi approksimiruemosti otnositelno sopryazhennosti nekotorykh svobodnykh polinilpotentnykh grupp”, XVI Vsesoyuznaya algebraicheskaya konferentsiya. Tezisy, ch. 2, Leningrad, 1981, 175

[4] Kolmakov Yu. A., Obobschenie teoremy Magnusa o vlozhenii, Rukopis dep. v VINITI 02.07.82, No 3445-82 Dep., Mosk. gosud. un-t, M., 18 s

[5] Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974 | MR | Zbl

[6] Neumann B. H., “Twisted wreath products of groups”, Arch. Math., 14:1 (1963), 1–6 | DOI | MR | Zbl

[7] Kholl F., “Nilpotentnye gruppy”, Sb. perevodov: Matematika, § 1, 12, 1968, 3–36

[8] Krouell R., Foks R., Vvedenie v teoriyu uzlov, Mir, M., 1967 | MR

[9] Remeslennikov V. N., “Sopryazhennost v politsiklicheskikh gruppakh”, Algebra i logika, 8:6 (1969), 712–725 | MR | Zbl

[10] Kassels Dzh., Vvedenie v geometriyu chisel, Mir, M., 1965 | MR

[11] Dunwoody M. J., “On verbal subgroups of free groups”, Arch. Math., 16 (1965), 153 | DOI | MR | Zbl

[12] Maltsev A. I., “O gomomorfizmakh na konechnye gruppy”, Uch. zap. Ivanovskogo gos. ped. in-ta, 18 (1958), 49–60 | MR