Embedding theorems for profinite groups

V. N. Remeslennikov

Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 367-382

Résumé

Suppose that the profinite group $G$ is an extension of $A$ by $H$. In this paper the profinite subgroups of the topological group of continuous maps from $H$ to $A$ are investigated. The results obtained are used to prove topological analogues for profinite groups of the Frobenius and Magnus embedding theorems. Moreover, a sufficient condition is formulated for a pro-$p$-group that is an extension of an abelian group by a finitely presented group to be finitely presented, in the language of complete tensor products of abelian pro-$p$-groups; and this condition is used to prove that a finitely generated metabelian pro-$p$-group is a subgroup of a finitely presented metabelian pro-$p$-group. Bibliography: 14 titles.