Algorithmic problems for free-abelian times free groups
We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of Zm×Fn. These tools are used to solve several algorithmic probl...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/20243 |
| Acesso em linha: | https://hdl.handle.net/2117/20243 https://dx.doi.org/10.1016/j.jalgebra.2013.04.033 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Group theory Free groups Abelian groups Automorphisms Automorphism Decision problem Free group Free-abelian group Grups, Teoria de Grups abelians Automorfismes 20E05 20k01 Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Resumo: | We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of Zm×Fn. These tools are used to solve several algorithmic problems for Zm×Fn: the membership problem, the isomorphism problem, the finite index problem, the subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem. |
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