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

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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. 
@article{IM2_1986_27_3_a8,
     author = {I. V. Andozhskii and V. M. Tsvetkov},
     title = {Analytic pro-$p$-groups of rank~$3$ and closed pro-$p$-groups of type~$(3,4)$},
     journal = {Izvestiya. Mathematics },
     pages = {593--599},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_3_a8/}
}
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%J Izvestiya. Mathematics 
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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/