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Computational problems in hyperbolic groups. (English) Zbl 1079.20060

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).

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
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References:

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