Olga Kharlampovich, Alexei Myasnikov, Vladimir Remeslennikov, Denis Serbin
February 22, 2008
In this paper we study exponential extensions of G which are finitely generated G -subgroups of the ℤ[ t ]-completion G ℤ[ t ] of a given CSA-group G . Using Bass–Serre theory we prove that exponential extensions of G can be obtained from subgroups of G by free constructions of a special type. As an application of this technique we describe the cohomological and homological dimensions of finitely generated fully residually free groups and give an algorithm to compute them.