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Subgroups of direct products of limit groups over coherent right-angled Artin groups
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Lopez de Gamiz Zearra, Jone (2022) Subgroups of direct products of limit groups over coherent right-angled Artin groups. PhD thesis, University of Warwick ; Universidad del País Vasco..
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WRAP_Theses_LopezdeGamizZearra_2022.pdf - Submitted Version - Requires a PDF viewer. Download (1119Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3861055
Abstract
During the last 40 years, a large body of work has been directed to study the connection between finiteness properties of groups and their algebraic and algorithmic properties. One of the early results is due to Baumslag and Roseblade, who showed that while finitely generated subgroups of the direct product of two free groups are wild and untractable, the finitely presented ones have nice algebraic and algorithmic properties. This work was widely extended during the years to the class of finitely presented residually free groups viewed as subgroups of direct products of limit groups.
In this thesis we continue this study and show that the good behaviour of finitely presented subgroups extends to the class of finitely presented residually Droms RAAGs. More precisely, we give a complete characterisation of finitely presented residually Droms RAAGs and we obtain a number of consequences related to decision problems, growth of homology and the Bieri-Neumann-Strebel-Renz invariants. We also study the subgroup structure of direct products of limit groups over Droms RAAGs depending on their finiteness properties. Finally, we initiate the study of finitely presented subgroups of direct products of 2-dimensional coherent RAAGs.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Finite groups, Free groups, Free products (Group theory), Artin algebras | ||||
Official Date: | May 2022 | ||||
Dates: |
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Institution: | University of Warwick ; Universidad del País Vasco. | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Casals-Ruiz, Montserrat ; Vogtmann, Karen, 1949- | ||||
Format of File: | |||||
Extent: | xiii, 161 pages : illustrations | ||||
Language: | eng |
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