Geodesic
On some classes of closed pro-$p$-groups
Izvestiya. Mathematics , Tome 9 (1975) no. 4, pp. 663-691.

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

This paper considers the problem of the finiteness of a pro-$p$-group $G$ with trivial Schur multiplicator (or closed pro-$p$-group) in the following three cases: (i) $G$ has 3 generators and 3 defining relations, $p\geqslant3$ and $G^p\supset(G,G)$; (ii) $G$ has 2 generators and 2 defining relations, $p\geqslant5$ and $G^p\supset(G,G,G)$; (iii) $G$ has 3 generators and 3 defining relations, $p\geqslant5$ and one of the relations lies in the fourth term of the Zassenhaus filtration. Bibliography: 19 items. 
@article{IM2_1975_9_4_a0,
     author = {I. V. Andozhskii},
     title = {On some classes of closed pro-$p$-groups},
     journal = {Izvestiya. Mathematics },
     pages = {663--691},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a0/}
}
TY  - JOUR
AU  - I. V. Andozhskii
TI  - On some classes of closed pro-$p$-groups
JO  - Izvestiya. Mathematics 
PY  - 1975
SP  - 663
EP  - 691
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a0/
LA  - en
ID  - IM2_1975_9_4_a0
ER  - 
%0 Journal Article
%A I. V. Andozhskii
%T On some classes of closed pro-$p$-groups
%J Izvestiya. Mathematics 
%D 1975
%P 663-691
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a0/
%G en
%F IM2_1975_9_4_a0
I. V. Andozhskii. On some classes of closed pro-$p$-groups. Izvestiya. Mathematics , Tome 9 (1975) no. 4, pp. 663-691. http://geodesic.mathdoc.fr/item/IM2_1975_9_4_a0/

[1] Shafarevich I. R., “Rasshireniya s zadannymi tochkami vetvleniya”, Publ. Math. JHES, 1964, no. 18, 295–316

[2] Vinberg E. B., “K teoreme o beskonechnomernosti assotsiativnoi algebry”, Izv. AN SSSR. Ser. matem., 29 (1965), 209–214 | MR | Zbl

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

[4] Koch H., “Zum Satz von Golod–Shafarevič”, Math. Nachr., 42 (1969), 321–333 | DOI | MR | Zbl

[5] Lazard M., “Groupes analytiques $p$-adiques”, Publ. Math. JHES, 1965, no. 26 | MR | Zbl

[6] Mennicke J., “Einige endliche Gruppen mit drei Erzengenden und drei Relationen”, Arch. Math., 10 (1959), 409–418 | DOI | MR | Zbl

[7] Skopin A. I., “Ideal sootnoshenii”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 80, 1965, 117–128 | MR | Zbl

[8] Macdonald J. D., “On a class of finitely presented groupes”, Canadian J. Math., 14 (1962), 602–614 | MR

[9] Skopin A. I., “O nekotorykh konechnykh gruppakh”, Zap. nauchn. seminarov Leningr. otd. Matem. in-ta AN SSSR, 31, 1973, 115–139 | MR | Zbl

[10] Andozhskii I. V., Tsvetkov V. M., “Ob odnoi serii konechnykh zamknutykh $p$-grupp”, Izv. AN SSSR. Ser. matem., 38 (1974), 278–290 | Zbl

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

[12] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl

[13] Dzhekobson N., Algebry Li, IL, M., 1964

[14] Andozhskii I. V., “O podgruppakh gruppy Demushkina”, Matem. zametki, 4:3 (1968), 349–354 | Zbl

[15] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR

[16] Maklein S., Gomologiya, Mir, M., 1966

[17] Kaplanskii I., Vvedenie v differentsialnuyu algebru, IL, M., 1959

[18] Serr Zh.-P., Kurs arifmetiki, Mir, M., 1972 | MR | Zbl

[19] Golod E. S., Shafarevich I. R., “O bashne polei klassov”, Izv. AN SSSR. Ser. matem., 28 (1964), 261–272 | MR | Zbl