仙人掌群、孪生群和直角阿尔丁群

IF 0.6 3区 数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-01-10 DOI:10.1007/s10801-023-01286-8
Paolo Bellingeri, Hugo Chemin, Victoria Lebed
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引用次数: 0

摘要

仙人掌群(J_n\ )目前正吸引着不同数学界的浓厚兴趣。这项工作探讨了它们与直角考克赛特群的关系,尤其是孪生群(Tw_n\ )和莫斯托沃伊的高斯图群(D_n\ ),这两个群更容易理解。具体来说,我们构建了一个从\(J_n\)到\(D_n\)的注入群1-循环,并证明了\(Tw_n\)(及其k叶广义)注入到\(J_n\)中。作为推论,我们解决了仙人掌群的字问题,确定了它们的扭转(只有偶数)和中心(微不足道),并回答了纯仙人掌群(PJ_n\ )的同样问题。此外,我们还得到了第一个非阿贝尔纯仙人掌群 \(PJ_4\) 的 1-relator 呈现。我们的工具主要来自组合群理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Cactus groups, twin groups, and right-angled Artin groups

Cactus groups \(J_n\) are currently attracting considerable interest from diverse mathematical communities. This work explores their relations to right-angled Coxeter groups and, in particular, twin groups \(Tw_n\) and Mostovoy’s Gauss diagram groups \(D_n\), which are better understood. Concretely, we construct an injective group 1-cocycle from \(J_n\) to \(D_n\) and show that \(Tw_n\) (and its k-leaf generalizations) inject into \(J_n\). As a corollary, we solve the word problem for cactus groups, determine their torsion (which is only even) and center (which is trivial), and answer the same questions for pure cactus groups, \(PJ_n\). In addition, we yield a 1-relator presentation of the first non-abelian pure cactus group \(PJ_4\). Our tools come mainly from combinatorial group theory.

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来源期刊
CiteScore
1.50
自引率
12.50%
发文量
94
审稿时长
6-12 weeks
期刊介绍: The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.
期刊最新文献
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