Profinite HNN-constructions
Wolfgang N. Herfort, Pavel A. Zalesskii Β· Journal of Group Theory Β· 2007
Let π be a class of finite groups closed under taking subgroups, quotients and extensions. We use a pro-π analogue of the HNN-construction, to show that every virtually torsion-free pro-π group G can be embedded in a pro-π group E such that every finite subgroup of E is, up to conjugation, contained in a finite subgroup of E isomorphic to the quotient G/F , where F is an open torsion-free normal subgroup of G . Moreover the virtual cohomological dimensions of G and E coincide. As a by-product we provide a structure theorem for cyclic p -extensions of free pro- p groups.