On two-generator subgroups of mapping torus groups

Publication Date

7-1-2025

Document Type

Article

Publication Title

Journal of the London Mathematical Society

Volume

112

Issue

1

DOI

10.1112/jlms.70226

Abstract

We prove that if (Formula presented.) is the mapping torus group of an injective endomorphism (Formula presented.) of a free group (Formula presented.) (of possibly infinite rank), then every two-generator subgroup (Formula presented.) of (Formula presented.) is either free or a (finitary) sub-mapping torus. As an application we show that if (Formula presented.) is a fully irreducible atoroidal automorphism, then every two-generator subgroup of (Formula presented.) is either free or has finite index in (Formula presented.).

Funding Number

850930

Funding Sponsor

European Research Council

Department

Mathematics and Statistics

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