Blasco García, Rubén
Martínez Pérez, Concepción (dir.) ; Cogolludo Agustín, José Ignacio (dir.)
Universidad de Zaragoza,
2019
Resumen: Right-angled Artin groups form an interesting family of groups both from an
algebraic and a topological point of view. There are a lot of well-known properties
of right-angled Artin groups: for example they are poly-free, locally
indicable, right orderable and residually finite. Besides, also many important
problems are well understood for these groups such as the word problem, the
rigidity problem, Serre's question or the K(pi, 1) conjecture.
In this thesis, we will study some of these properties for a bigger and
interesting subfamily of Artin groups: even Artin groups. We generalize
many of these properties either for even Artin groups in full genarility or for
some big and interesting subfamilies.
In particular, we prove that even Artin groups of FC type and large even
Artin groups are poly-free (which, as we will see, implies that they are also
locally indicable and right orderable) and that even Artin groups of FC type
and general Artin groups based on trees are residually finite. Finally, we
answer Serre's question for the whole family of even Artin groups.
Resumen (otro idioma):
algebraic and a topological point of view. There are a lot of well-known properties
of right-angled Artin groups: for example they are poly-free, locally
indicable, right orderable and residually finite. Besides, also many important
problems are well understood for these groups such as the word problem, the
rigidity problem, Serre's question or the K(pi, 1) conjecture.
In this thesis, we will study some of these properties for a bigger and
interesting subfamily of Artin groups: even Artin groups. We generalize
many of these properties either for even Artin groups in full genarility or for
some big and interesting subfamilies.
In particular, we prove that even Artin groups of FC type and large even
Artin groups are poly-free (which, as we will see, implies that they are also
locally indicable and right orderable) and that even Artin groups of FC type
and general Artin groups based on trees are residually finite. Finally, we
answer Serre's question for the whole family of even Artin groups.
Resumen (otro idioma):
Pal. clave: grupos generalidades ; geometria algebraica
Titulación: Programa de Doctorado en Matemáticas y Estadística
Plan(es): Plan 490
Departamento: Matemáticas
Nota: Presentado: 03 09 2019
Nota: Tesis-Univ. Zaragoza, Matemáticas, 2019
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Registro creado el 2020-01-16, última modificación el 2021-05-20
