Structure of quasiconvex virtual joins

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-04-04 DOI:10.1112/topo.70021

Lawk Mineh

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引用次数: 0

Abstract

Let $G$ be a relatively hyperbolic group and let $Q$ and $R$ be relatively quasiconvex subgroups. It is known that there are many pairs of finite index subgroups $Q^{'} ⩽_{f} Q$ and $R^{'} ⩽_{f} R$ such that the subgroup join $⟨ Q^{'}, R^{'} ⟩$ is also relatively quasiconvex, given suitable assumptions on the profinite topology of $G$ . We show that the intersections of such joins with maximal parabolic subgroups of $G$ are themselves joins of intersections of the factor subgroups $Q^{'}$ and $R^{'}$ with maximal parabolic subgroups of $G$ . As a consequence, we show that quasiconvex subgroups whose parabolic subgroups are almost compatible have finite index subgroups whose parabolic subgroups are compatible, and provide a combination theorem for such subgroups.

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拟凸虚连接的结构

设G $G$为相对双曲群，设Q $Q$和R $R$为相对拟凸子群。已知有许多对有限指标子群Q ‘≤f Q $Q^{\prime } \leqslant _f Q$和R ’≤f R $R^{\prime } \leqslant _f R$使得子群连接⟨Q '，R '⟩$\langle Q^{\prime }, R^{\prime } \rangle$也是相对拟凸的，给定对G $G$的无限拓扑的适当假设。我们证明了与G $G$的极大抛物子群的这种联接的交集本身就是因子子群Q ‘ $Q^{\prime }$和R ’的交集的交集。$R^{\prime }$与G的极大抛物子群$G$。因此，我们证明了抛物子群几乎相容的拟凸子群具有抛物子群相容的有限指数子群，并给出了这类子群的组合定理。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.