Subgroups of right-angled Coxeter groups via Stallings-like techniques

Dani Pallavi; Levcovitz Ivan

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Subgroups of right-angled Coxeter groups via Stallings-like techniques

机译：Subgroups of right-angled Coxeter groups via Stallings-like techniques

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摘要

We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We use completions to show that reflection subgroups are quasiconvex, as are one-ended Coxeter subgroups of a 2-dimensional RACG. We provide an algorithm that determines whether a given one-ended, 2-dimensional RACG is isomorphic to some finite-index subgroup of another given RACG. In addition, we answer several algorithmic questions regarding quasiconvex subgroups. Finally, we give a new proof of Haglund's result that quasiconvex subgroups of RACGs are separable.

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《journal of combinatorial algebra》 |2021年第3期|237-295|共59页
作者
Dani Pallavi; Levcovitz Ivan;
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作者单位

Louisiana State Univ;

Techion Israel Inst Technol;

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正文语种英语
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Right-angled Coxeter groups; quasiconvex subgroups; algorithmic problems; GRAPH; COMMENSURABILITY; PERIMETER; AMALGAMS; PROPERTY; INDEX;

Subgroups of right-angled Coxeter groups via Stallings-like techniques

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