TY - JOUR
T1 - Exponential extensions of groups
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
AU - Remeslennikov, Vladimir
AU - Serbin, Denis
PY - 2008/1/1
Y1 - 2008/1/1
N2 - In this paper we study exponential extensions of G which are finitely generated G-subgroups of the ℤ[t]-completion Gℤ[t] of a given CSA-group G. Using BassSerre 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.
AB - In this paper we study exponential extensions of G which are finitely generated G-subgroups of the ℤ[t]-completion Gℤ[t] of a given CSA-group G. Using BassSerre 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.
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U2 - 10.1515/JGT.2008.008
DO - 10.1515/JGT.2008.008
M3 - Article
AN - SCOPUS:39749191212
SN - 1433-5883
VL - 11
SP - 119
EP - 140
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 1
ER -