Canonical representatives and equations in hyperbolic groups

E. Rips*, Z. Sela

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


We use canonical representatives in hyperbolic groups to reduce the theory of equations in (torsion-free) hyperbolic groups to the theory in free groups. As a result we get an effective procedure to decide if a system of equations in such groups has a solution. For free groups, this question was solved by Makanin [Ma]|and Razborov [Ra]. The case of quadratic equations in hyperbolic groups has already been solved by Lysenok [Ly]. Our whole construction plays an essential role in the solution of the isomorphism problem for (torsion-free) hyperbolic groups ([Se1],[Se2]).

Original languageAmerican English
Pages (from-to)489-512
Number of pages24
JournalInventiones Mathematicae
Issue number1
StatePublished - Dec 1995


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