On two-generator subgroups of mapping torus groups

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-08 DOI:10.1112/jlms.70226

Naomi Andrew, Edgar A. Bering IV, Ilya Kapovich, Stefano Vidussi, Peter Shalen

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引用次数: 0

Abstract

We prove that if $G_{φ} = ⟨ F, t | t x t^{- 1} = φ (x), x \in F ⟩$ is the mapping torus group of an injective endomorphism $φ : F \to F$ of a free group $F$ (of possibly infinite rank), then every two-generator subgroup $H$ of $G_{φ}$ is either free or a (finitary) sub-mapping torus. As an application we show that if $φ \in Out (F_{r})$ is a fully irreducible atoroidal automorphism, then every two-generator subgroup of $G_{φ}$ is either free or has finite index in $G_{φ}$ .

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关于映射环面群的二生成子群

我们证明如果G φ =⟨F，T | T x T−1 = φ (x)，x∈F⟩$G_\varphi =\langle F, t| t x t^{-1} =\varphi (x), x\in F\rangle$是一个内射自同态φ的映射环面群：F→F $\varphi: F\rightarrow F$的自由群F $F$（可能是无限秩），则G φ $G_\varphi$的每个二生成子群H $H$要么是自由的，要么是一个（有限的）子映射环面。作为一个应用，我们证明了如果φ∈Out (F r) $\varphi \in \mbox{Out}(F_r)$是一个完全不可约的自同构，则G φ $G_\varphi$的每一个二生成子群要么是自由的，要么在G φ $G_\varphi$上有有限的索引。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.