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math.GR2024
Geodesic languages for rational subsets and conjugates in virtually free groups
André Carvalho, Pedro V. Silva
We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that th…
math.GR2024
Free-abelian by free groups: homomorphisms and algorithmic explorations
André Carvalho, Jordi Delgado
We obtain an explicit description of the endomorphisms of free-abelian by free groups together with a characterization of when they are injective and surjective. As a consequence w…
math.GR2024
Orbit problems for free-abelian times free groups and related families
André Carvalho, Jordi Delgado
We prove that the Brinkmann Problems (BrP & BrCP) and the twisted-conjugacy Problem (TCP) are decidable for any endomorphism of a free-abelian times free (FATF) group Fn x Z^m. Fur…