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Abstract
Let 𝒞 be a class of finite groups closed under taking subgroups, quotients and extensions. We use a pro-𝒞 analogue of the HNN-construction, to show that every virtually torsion-free pro-𝒞 group G can be embedded in a pro-𝒞 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.
Received: 2006-11-24
Revised: 2007-03-27
Published Online: 2008-01-04
Published in Print: 2007-11-20
© Walter de Gruyter
