On Quasiconvexity and Relative Hyperbolic Structures
On Quasiconvexity and Relative Hyperbolic Structures
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发表时间：
2008-11
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通讯作者：
Eduardo Martínez-Pedroza
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作者：
Eduardo Martínez-Pedroza
设G是关于子群A的集合的双曲群，它也是关于子群B的集合的双曲群。假设集合A包含B，我们刻画了对于G的子群，当关于A的拟凸性蕴含关于B的拟凸性时，我们还证明了相对于B的拟凸性蕴含着关于A的拟凸性。
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. Some applications are discussed.