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. 
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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/

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