辫状群 m$ 级同余子群的生成器

arXiv - MATH - Group Theory Pub Date : 2024-09-15 DOI:arxiv-2409.09612

Ishan Banerjee, Peter Huxford

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引用次数: 0

摘要

对于 $m\geq1$ 和 $n\geq5$，我们证明辫子群 $B_n$ 的 $m$ 级全等子群 $B_n[m]$是由半捻子的 $m$ 次幂和辫子托雷利群生成的。这解决了Margalit的一个问题，推广了Assion、Brendle--Margalit、Nakamura、Stylianakis和Wajnryb的工作。

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Generators for the level $m$ congruence subgroups of braid groups

We prove for $m\geq1$ and $n\geq5$ that the level $m$ congruence subgroup $B_n[m]$ of the braid group $B_n$ associated to the integral Burau representation $B_n\to\mathrm{GL}_n(\mathbb{Z})$ is generated by $m$th powers of half-twists and the braid Torelli group. This solves a problem of Margalit, generalizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and Wajnryb.

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arXiv - MATH - Group Theory

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