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Finding relative hyperbolic structures
Author(s) -
Dahmani François
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn018
Subject(s) - cayley graph , abelian group , mathematics , class (philosophy) , relatively hyperbolic group , graph , presentation (obstetrics) , constant (computer programming) , pure mathematics , group (periodic table) , algebra over a field , discrete mathematics , hyperbolic manifold , computer science , hyperbolic function , mathematical analysis , artificial intelligence , physics , quantum mechanics , medicine , programming language , radiology
We propose an algorithm that recognizes relatively hyperbolic groups from a compatible relative presentation, and even from an arbitrary finite presentation when the parabolic subgroups are abelian. Moreover, it computes important characteristic features such as the hyperbolicity constant of the coned‐off Cayley graph. This tool allows us to unify solutions to decision problems for individual groups in the class of relatively hyperbolic groups with abelian parabolics, into a unique solution suitable for every group in the class.