具有固定间隔交换变换的关系

Pub Date : 2023-12-15 DOI:10.1007/s10711-023-00868-x

Magali Jay

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引用次数: 0

摘要

摘要我们研究了所有区间交换变换（IET）群。卡托克问它是否包含一个自由子群。我们证明，对于每一个 IET S，都存在一个可容许 IET 的密集开集 \(\Omega (S)\) ，使得由 S 和任何 \(T\in \Omega (S)\) 生成的群不是秩为 2 的自由群。这扩展了 Dahmani 等人的一个结果（Groups Geom Dyn 7(4):883-910, 2013）：IET([0;1))的一般元素对所生成的群不是自由的（假设对底层置换有合适的条件）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Relations with a fixed interval exchange transformation

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Relations with a fixed interval exchange transformation

Abstract

We study the group of all interval exchange transformations (IETs). Katok asked whether it contains a free subgroup. We show that for every IET S, there exists a dense open set \(\Omega (S)\) of admissible IETs such that the group generated by S and any \(T\in \Omega (S)\) is not free of rank 2. This extends a result by Dahmani et al. (Groups Geom Dyn 7(4):883–910, 2013): the group generated by a generic pair of elements of IET([0;1)) is not free (assuming a suitable condition on the underlying permutation).

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