Exponential extensions of groups

Olga Kharlampovich; Alexei Myasnikov; Vladimir Remeslennikov; Denis Serbin

doi:10.1515/JGT.2008.008

Exponential extensions of groups

Olga Kharlampovich
, Alexei Myasnikov
, Vladimir Remeslennikov
, Denis Serbin

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 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.

Original language	English
Pages (from-to)	119-140
Number of pages	22
Journal	Journal of Group Theory
Volume	11
Issue number	1
DOIs	https://doi.org/10.1515/JGT.2008.008
State	Published - 1 Jan 2008

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abstract = "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.",

author = "Olga Kharlampovich and Alexei Myasnikov and Vladimir Remeslennikov and Denis Serbin",

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AU - Kharlampovich, Olga

AU - Myasnikov, Alexei

AU - Remeslennikov, Vladimir

AU - Serbin, Denis

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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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DO - 10.1515/JGT.2008.008

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SP - 119

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JO - Journal of Group Theory

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Exponential extensions of groups

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