有限性质和相对双曲群

IF 0.9 3区 数学 Q2 MATHEMATICS
Harsh Patil
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引用次数: 0

摘要

我们证明了F n$ F_n$和FP n$ FP_n$对一个相对双曲群成立当且仅当它们对所有外围子群成立。作为一个应用,我们证明了至少存在可数多个不同的拟等距类,它们是F n$ F_n$型,但不是F n + 1型$F_{n+1}$和类似的FP n$ FP_n$类型,而不是FP n+1$FP_{n+1}$适用于所有正整数n$ n$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Finiteness properties and relatively hyperbolic groups

Finiteness properties and relatively hyperbolic groups

Finiteness properties and relatively hyperbolic groups

Finiteness properties and relatively hyperbolic groups

Finiteness properties and relatively hyperbolic groups

We show that properties F n $F_n$ and F P n $FP_n$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended non-amenable groups that are type F n $F_n$ but not F n + 1 $F_{n+1}$ and similarly of type F P n $FP_n$ and not F P n + 1 $FP_{n+1}$ for all positive integers n $n$ .

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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
198
审稿时长
4-8 weeks
期刊介绍: Published by Oxford University Press prior to January 2017: http://blms.oxfordjournals.org/
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