Geodesic
Analytic pro-$p$-groups of rank $3$ and closed pro-$p$-groups of type $(3,4)$
Izvestiya. Mathematics, Tome 27 (1986) no. 3, pp. 593-599 
I. V. Andozhskii; V. M. Tsvetkov. Analytic pro-$p$-groups of rank $3$ and closed pro-$p$-groups of type $(3,4)$. Izvestiya. Mathematics, Tome 27 (1986) no. 3, pp. 593-599. http://geodesic.mathdoc.fr/item/IM2_1986_27_3_a8/
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     title = {Analytic pro-$p$-groups of rank~$3$ and closed pro-$p$-groups of type~$(3,4)$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a pro-$p$-group of type $(3,4)$ that is closed (in the sense of Schur) with an elementary Abelian commutator-factor group is always finite for $p\geqslant7$. The proof uses the classification of analytic pro-$p$-groups of rank $3$. Bibliography: 7 titles.

[1] Andozhskii I. V., “O nekotorykh klassakh zamknutykh pro-$p$-grupp”, Izv. AN SSSR. Ser. matem., 39:4 (1975), 707–738 | MR | Zbl

[2] Vinberg E. B., “K teoreme o beskonechnomernosti assotsiativnoi aglebry”, Izv. AN SSSR. Ser. matem., 29:1 (1965), 209–214 | MR | Zbl

[3] Golod E. S., Shafarevich I. R., “O bashne polei klassov”, Izv. AN SSSR. Ser. matem., 28:2 (1964), 261–272 | MR | Zbl

[4] Serr Zh.-P., Komologiya Galua, Mir, M., 1968 | MR

[5] Shafarevich I. R., “Rasshireniya s zadannymi tochkami vetvleniya”, Publ. Math. IHES, 18 (1964), 71–95

[6] Lazard M., “Groupes analytiques $p$-adiques”, Publ. Math. IHES, 26 (1965) | MR | Zbl

[7] Schur J., “Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen”, J. rein und angew. Math., 132 (1907), 85–137 | Zbl