TY - JOUR
T1 - Actions, length functions, and non-archimedean words
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
AU - Serbin, Denis
PY - 2013/3
Y1 - 2013/3
N2 - In this paper we survey recent developments in the theory of groups acting on Λ-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented Λ-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups.
AB - In this paper we survey recent developments in the theory of groups acting on Λ-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented Λ-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups.
KW - Group actions on trees
KW - length functions
KW - relatively hyperbolic groups
KW - Λ-trees
UR - http://www.scopus.com/inward/record.url?scp=84875335638&partnerID=8YFLogxK
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U2 - 10.1142/S0218196713400031
DO - 10.1142/S0218196713400031
M3 - Review article
AN - SCOPUS:84875335638
SN - 0218-1967
VL - 23
SP - 325
EP - 455
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
IS - 2
ER -