Analytic pro-$p$-groups of rank $3$ and closed pro-$p$-groups of type $(3,4)$

I. V. Andozhskii, V. M. Tsvetkov


Abstract: 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.

UDC: 519.444

MSC: 20D10, 20E18

Received: 14.01.1983

 English version: Mathematics of the USSR-Izvestiya, 1986, 27:3, 593–599

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