On Products of Quasiconvex Subgroups in Hyperbolic Groups

Details On Products of Quasiconvex Subgroups in Hyperbolic Groups On Products of Quasiconvex Subgroups in Hyperbolic Groups

2004-04-21

arxiv.org/abs/math/0404397v1

Intern. J. of Algebra and Comput. 14 (2004), no. 2, pp. 173-195

Mathematics

Group Theory

22 pages, 6 figures. To appear in Intern. J. of Algebra and Comput

Scientific paper

An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. A known example is the class of all quasiconvex subgroups. However, not much is yet learned about the structure of arbitrary quasiconvex subsets. In this work we study the properties of products of quasiconvex subgroups; we show that such sets are quasiconvex, their finite intersections have a similar algebraic representation and, thus, are quasiconvex too.

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