具有两个发生器的群的表面群猜想

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2022-02-22 DOI:10.4310/mrl.2023.v30.n1.a5

Giles Gardam, Dawid Kielak, Alan D. Logan

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引用次数: 2

摘要

表面群猜想是关于在单相关群中识别表面群的陈述，使用它们的有限指数子群或所有子群的结构。我们在两个发电机的情况下解决了这些猜想。更一般地，我们证明了每一个具有无限索引子群自由的双生单相关群本身要么是自由的，要么是表面群。

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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The Surface Group Conjectures for groups with two generators

The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case. More generally, we prove that every two-generator one-relator group with every infinite-index subgroup free is itself either free or a surface group.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.