Some remarks on profinite HNN extensions (Q1320025)

It is shown that every profinite group \(G\) with only countably many open subgroups embeds in a 2-generated profinite group \(E\) in which all torsion elements are conjugate to elements of \(G\). The same result is proved in the category of pro-\(p\)-groups. The construction of \(E\) is in section 2 of the paper. In section 1 the kernel of the natural homomorphism of an abstract HNN-extension of profinite (resp. pro-\(p\)) groups to the profinite (resp. pro-\(p\)) HNN-extension of the same groups is studied. It is used later for the construction of \(E\).