Day, JD and Reidenbach, D (2022) Unambiguous Injective Morphisms in Free Groups. Information and Computation, 289A (104946). ISSN 0890-5401

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A morphism g is ambiguous with respect to a word u if there exists a second morphism h 6= g such that g(u) = h(u). Otherwise g is unambiguous with respect to u. Thus unambiguous morphisms are those for which the structure of the morphism is preserved in the image. Ambiguity has so far been studied for morphisms of free monoids, where several characterisations exist for the set of words u permitting an (injective) unambiguous morphism. In the present paper, we consider ambiguity of morphisms of free groups, and consider possible analogies to the existing characterisations in the free monoid. While a direct generalisation results in a trivial situation where all morphisms are ambiguous, we discuss some natural and well-motivated reformulations, and provide a characterisation of words in a free group that
permit a morphism which is “as unambiguous as possible”.

Item Type: Article
Additional Information: © 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (
Uncontrolled Keywords: Free groups; Automorphisms; Ambiguity of morphisms
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 26 Jul 2022 12:01
Last Modified: 20 Mar 2023 13:51

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