Geodesic
Embedding theorems for profinite groups
Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 367-382.

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

Suppose that the profinite group $G$ is an extension of $A$ by $H$. In this paper the profinite subgroups of the topological group of continuous maps from $H$ to $A$ are investigated. The results obtained are used to prove topological analogues for profinite groups of the Frobenius and Magnus embedding theorems. Moreover, a sufficient condition is formulated for a pro-$p$-group that is an extension of an abelian group by a finitely presented group to be finitely presented, in the language of complete tensor products of abelian pro-$p$-groups; and this condition is used to prove that a finitely generated metabelian pro-$p$-group is a subgroup of a finitely presented metabelian pro-$p$-group. Bibliography: 14 titles. 
@article{IM2_1980_14_2_a8,
     author = {V. N. Remeslennikov},
     title = {Embedding theorems for profinite groups},
     journal = {Izvestiya. Mathematics },
     pages = {367--382},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a8/}
}
TY  - JOUR
AU  - V. N. Remeslennikov
TI  - Embedding theorems for profinite groups
JO  - Izvestiya. Mathematics 
PY  - 1980
SP  - 367
EP  - 382
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a8/
LA  - en
ID  - IM2_1980_14_2_a8
ER  - 
%0 Journal Article
%A V. N. Remeslennikov
%T Embedding theorems for profinite groups
%J Izvestiya. Mathematics 
%D 1980
%P 367-382
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a8/
%G en
%F IM2_1980_14_2_a8
V. N. Remeslennikov. Embedding theorems for profinite groups. Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 367-382. http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a8/

[1] Dzh. Kassels, A. Frelikh (red.), Algebraicheskaya teoriya chisel, Mir, M., 1969

[2] Burbaki N., Algebra. Algebraicheskie struktury, lineinaya i polilineinaya algebra, Fizmatgiz, M., 1962

[3] Zarisskii O., Samyuel P., Kommutativnaya algebra, t. 2, Mir, M., 1963

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

[5] Kokh X., Teoriya Galua $p$-rasshirenii, Mir, M., 1973 | MR

[6] Neimann X., Mnogoobraziya grupp, Mir, M., 1969 | MR

[7] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973 | MR | Zbl

[8] Remeslennikov V. N., Tezisy dokladov 4-i Kazakhstanskoi mezhvuzovskoi nauchnoi konferentsii po matematike i mekhanike, Chast I. Matematika, Alma-Ata, 1971 | Zbl

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

[10] Remeslennikov V. N., Doktorskaya dissertatsiya, Novosibirsk, 1974 | Zbl

[11] Serr Zh.-P., Kogomologii Galua, Mir, M., 1968 | MR

[12] Baumslag G., “Subgroups of finitely presented metabelian groups”, J. Austral. Math. Soc., 16 (1973), 98–110 | DOI | MR | Zbl

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

[14] Hall Ph., “Finiteness conditions for soluble groups”, Proc. London Math. Soc., 4 (1954), 419–436 | DOI | MR | Zbl