Geodesic
On Metanilpotent Varieties of Groups
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 875-877

Voir la notice de l'article provenant de la source Cambridge University Press

Let denote the variety of all groups which are extensions of a nilpotent-of-class-c group by a nilpotent-of-class-d group, and let denote the variety of all metabelian groups. The main result of this paper is the following theorem.THEOREM. Let be a subvariety of which does not contain . Then every -group is an extension of a group of finite exponent by a nilpotent group by a group of finite exponent. In particular, a finitely generated torsion-free -group is a nilpotent-by-finite group.This generalizes the main theorem of Ŝmel′kin [4], where the same result is proved for subvarieties of , where is the variety of abelian groups. See also Lewin and Lewin [2] for a related discussion. 
Gupta, Narain. On Metanilpotent Varieties of Groups. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 875-877. doi: 10.4153/CJM-1970-099-2
@article{10_4153_CJM_1970_099_2,
     author = {Gupta, Narain},
     title = {On {Metanilpotent} {Varieties} of {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {875--877},
     year = {1970},
     volume = {22},
     number = {4},
     doi = {10.4153/CJM-1970-099-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-099-2/}
}
TY  - JOUR
AU  - Gupta, Narain
TI  - On Metanilpotent Varieties of Groups
JO  - Canadian journal of mathematics
PY  - 1970
SP  - 875
EP  - 877
VL  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-099-2/
DO  - 10.4153/CJM-1970-099-2
ID  - 10_4153_CJM_1970_099_2
ER  - 
%0 Journal Article
%A Gupta, Narain
%T On Metanilpotent Varieties of Groups
%J Canadian journal of mathematics
%D 1970
%P 875-877
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-099-2/
%R 10.4153/CJM-1970-099-2
%F 10_4153_CJM_1970_099_2

[1] 1. Gupta, N. D., Newman, M. F., and Tobin, S. J., On metabelian groups of prime-power exponent, Proc. Roy. Soc. Ser. A 302 (1968), 237–242. Google Scholar

[2] 2. Jacques, Lewin and Tekla Lewin, , Semigroup laws in varieties of solvable groups, Proc. Cambridge Philos. Soc. 65 (1969), 1–9. Google Scholar

[3] 3. Hanna, Neumann, Varieties of groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37 (Springer-Verlag, New York, 1967). Google Scholar

[4] 4. Smel'kin, A. L., On soluble group mrieties, Soviet Math. Dokl. 9 (1968), 100–103. (English translation) Google Scholar

Cité par Sources :