Marshall, Joseph Computational problems in hyperbolic groups. (English) Zbl 1079.20060 Int. J. Algebra Comput. 15, No. 1, 1-13 (2005). Summary: We describe an algorithm due to Eric Swenson for testing quasi-convex subgroups of hyperbolic groups for near malnormality. We go on to discuss some strategies for the practical implementation of this algorithm and consider an example. We then show that the methods of Swenson’s algorithm extend to give practical solutions to the conjugacy problem for infinite order elements, and to the normalizer and centralizer problems for subgroups satisfying appropriate conditions. The results are presented here in outline – all the algorithms are described in more detail in the author’s PhD thesis (University of Warwick, 2001). Cited in 2 Documents MSC: 20F67 Hyperbolic groups and nonpositively curved groups 20E07 Subgroup theorems; subgroup growth 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 68W30 Symbolic computation and algebraic computation Keywords:hyperbolic groups; malnormal subgroups; conjugacy problem; centralizers; normalizers; algorithms PDFBibTeX XMLCite \textit{J. Marshall}, Int. J. Algebra Comput. 15, No. 1, 1--13 (2005; Zbl 1079.20060) Full Text: DOI References: [1] J. M. Alonso, Group Theory from a Geometrical Viewpoint, ed. H. Short (World Scientific, 1990) pp. 3–63. [2] Bestvina M., J. Differential Geom. 35 pp 85– · Zbl 0724.57029 · doi:10.4310/jdg/1214447806 [3] Epstein D. B. A., Word Processing in Groups (1992) [4] DOI: 10.1007/BF01233430 · Zbl 0714.20016 · doi:10.1007/BF01233430 [5] DOI: 10.2307/2944334 · Zbl 0744.20035 · doi:10.2307/2944334 [6] DOI: 10.1007/978-1-4684-2001-2_9 · doi:10.1007/978-1-4684-2001-2_9 [7] DOI: 10.1007/BF01884301 · Zbl 0834.20040 · doi:10.1007/BF01884301 [8] Smith G. W., IEEE Trans. Circuits Syst. 22 pp 9– · doi:10.1109/TCS.1975.1083961 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.