Computation of endo-fixed closures in free-abelian times free groups

In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup H of a FATF group G , decides whether H is the fixed subgroup of some (finite) family of endomorphisms of G and...

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Detalles Bibliográficos
Autores: Roy, Mallika|||0000-0002-9730-5980, Ventura Capell, Enric|||0000-0003-3519-4135
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/446199
Acceso en línea:https://hdl.handle.net/2117/446199
https://dx.doi.org/10.1515/forum-2023-0471
Access Level:acceso abierto
Palabra clave:Free-abelian times free
Endomorphism
Fixed subgroup
Endo-fixed closure
Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups
Classificació AMS::20 Group theory and generalizations::20K Abelian groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
Descripción
Sumario:In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup H of a FATF group G , decides whether H is the fixed subgroup of some (finite) family of endomorphisms of G and, in the affirmative case, finds such a family. The algorithm combines both combinatorial and algebraic methods.