性质FW和群的环积:使用Schreier图的一种简单方法

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2022-12-01 DOI:10.1016/j.exmath.2022.07.001

Paul-Henry Leemann , Grégoire Schneeberger

引用次数: 2

摘要

集团财产FW位于著名的哈萨克斯坦财产(T)和Serre财产FA之间。在许多表征中，对于有限生成的群，可以将其定义为所有Schreier图都是单向的。由Y. cornlier的工作得出，当且仅当G和H都具有FW性质且X是有限的，有限生成的环积G≤XH具有FW性质。本文的目的是用Schreier图给出这一事实的初等、直接和明确的证明。

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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Property FW and wreath products of groups: A simple approach using Schreier graphs

The group property FW stands in-between the celebrated Kazhdan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended.

It follows from the work of Y. Cornulier that a finitely generated wreath product $G ≀_{X} H$ has property FW if and only if both $G$ and $H$ have property FW and $X$ is finite. The aim of this paper is to give an elementary, direct and explicit proof of this fact using Schreier graphs.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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