Geodesic
The variety of metabelian $\mathscr D$-groups
Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 759-781.

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

It is proved that an arbitrary metabelian $R$-group is imbeddable in a metabelian $\mathscr D$-group. Varieties consisting of metabelian $\mathscr D$-groups are described and a number of theorems on the structure of a free metabelian $\mathscr D$-group are obtained. A certain specially defined ring – an analog of the group ring – plays an essential role in the proofs. 
@article{IM2_1972_6_4_a4,
     author = {Yu. V. Kuz'min},
     title = {The variety of metabelian $\mathscr D$-groups},
     journal = {Izvestiya. Mathematics },
     pages = {759--781},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/}
}
TY  - JOUR
AU  - Yu. V. Kuz'min
TI  - The variety of metabelian $\mathscr D$-groups
JO  - Izvestiya. Mathematics 
PY  - 1972
SP  - 759
EP  - 781
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/
LA  - en
ID  - IM2_1972_6_4_a4
ER  - 
%0 Journal Article
%A Yu. V. Kuz'min
%T The variety of metabelian $\mathscr D$-groups
%J Izvestiya. Mathematics 
%D 1972
%P 759-781
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/
%G en
%F IM2_1972_6_4_a4
Yu. V. Kuz'min. The variety of metabelian $\mathscr D$-groups. Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 759-781. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/

[1] Baumslag G., “Some aspects of groups with unique roots”, Acta Math., 104 (1960), 217–303 | DOI | MR | Zbl

[2] Baumslag G., “Wreath products and $p$-groups”, Proc. Cambr. Phil. Soc., 55 (1959), 224–231 | DOI | MR | Zbl

[3] Maltsev A. I., “Nilpotentnye gruppy bez krucheniya”, Izv. AN SSSR. Ser. matem., 13 (1949), 201–212

[4] Shmelkin A. I., “Nilpotentnye proizvedeniya i nilpotentnye gruppy bez krucheniya”, Sib. matem. zh., 3 (1962), 625–640

[5] Neumann B. H., “Adjunction of elements to groups”, J. London Math. Soc., 18 (1943), 4–11 | DOI | MR | Zbl

[6] Baumslag G., “A generalisation of a theorem of Malcev”, Arch. Math., 12 (1961), 405–408 | DOI | MR | Zbl

[7] Kargapolov M. I., Merzlyakov Yu. I., Remeslennikov V. N., “O popolnenii grupp”, Dokl. AN SSSR, 134:3 (1960), 518–520 | MR | Zbl

[8] Neiman X., Mnogoobraziya grupp, Mir, M., 1969 | MR

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

[10] Shmelkin A. L., “O razreshimykh mnogoobraziyakh grupp”, Dokl. AN SSSR, 178:2 (1968), 307–310

[11] Shmelkin A. L., “Svobodnye polinilpotentnye gruppy”, Izv. AN SSSR. Ser. matem., 28 (1964), 91–122

[12] Shmelkin A. L., “O razreshimykh proizvedeniyakh grupp”, Sib. matem. zh., 6 (1965), 212–220

[13] Nielsen J., “Die Isomorphismen der allgemeinen, unendlicher Gruppe mit zwei Erzeugenden”, Math. Ann., 78 (1917), 385–387 | DOI | MR

[14] Bachmuth S., “Automorphisms of free metabelian groups”, Trans. Amer. Math. Soc., 118 (1965), 93–104 | DOI | MR | Zbl

[15] Shmelkin A. L., “Spleteniya i mnogoobraziya grupp”, Izv. AN SSSR. Ser. matem., 29 (1965), 149–170

[16] Shmelkin A. L., “Zamechanie k rabote:A. L. Shmelkin, Spleteniya i mnogoobraziya grupp”, Izv. AN SSSR. Ser. matem., 31 (1967), 443–444

[17] Shmelkin A. L., “Spleteniya algebr Li i ikh primenenie v teorii grupp”, Desyatyi vsesoyuznyi Algebraicheskii kollokvium (rezyume soobschenii i dokladov), tom I, Novosibirsk, 1969

[18] Shmelkin A. L., “Dva zamechaniya o svobodnykh razreshimykh gruppakh”, Alg. i log. seminar, 1967, 95–110

[19] Magnus W., Karrass A., Solitar D., Combinatorial group theory, New York, London, Sydney, 1966 | MR