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- Title
Irreducibility of a free group endomorphism is a mapping torus invariant.
- Authors
Mutanguha, Jean Pierre
- Abstract
We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall-Kapovich-Leininger. We further prove that being irreducible and atoroidal is a commensurability invariant. The invariance follows from an algebraic characterization of ascending HNN extensions that determines exactly when their defining endomorphisms are irreducible and atoroidal; specifically, we show that the endomorphism is irreducible and atoroidal if and only if the ascending HNN extension has no infinite index subgroups that are ascending HNN extensions.
- Subjects
FREE groups; TORUS; ENDOMORPHISMS
- Publication
Commentarii Mathematici Helvetici, 2021, Vol 96, Issue 1, p47
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/506