虚自由群的基本子群

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2021-12-06 DOI:10.4171/ggd/638

Simon André

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引用次数: 0

摘要

给出有限生成虚自由群的基本子群(一阶逻辑意义上的)的描述。特别地，我们恢复了有限生成自由群的初等子群是自由因子的事实。此外，有人给出了一种算法，该算法将几乎自由的群$G$和$G$的有限子集$X$的有限表示作为输入，并确定$X$生成的$G$的子群是否为$\forall\exists$ -初等。我们还证明了等式诺瑟群在自身中的每一个初等嵌入都是一个自同构。

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Elementary subgroups of virtually free groups

We give a description of elementary subgroups (in the sense of first-order logic) of finitely generated virtually free groups. In particular, we recover the fact that elementary subgroups of finitely generated free groups are free factors. Moreover, one gives an algorithm that takes as input a finite presentation of a virtually free group $G$ and a finite subset $X$ of $G$, and decides if the subgroup of $G$ generated by $X$ is $\forall\exists$-elementary. We also prove that every elementary embedding of an equationally noetherian group into itself is an automorphism.

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.