Stallings automata for free-times-abelian groups : intersections and index
Delgado Rodríguez, Jordi ![ORCID Identifier](/img/uab/orcid.ico)
(Universidad del País Vasco. Departamento de Matemáticas)
Ventura, Enric ![ORCID Identifier](/img/uab/orcid.ico)
(Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Date: |
2022 |
Abstract: |
We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i. e. , automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which-as it happens in the free group-is computable in the finitely generated case. This approach provides a neat geometric description of (even non-(finitely generated)) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals, respectively. |
Rights: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Subject: |
Free group ;
Free-abelian group ;
Direct product ;
Subgroup ;
Intersection ;
Stallings ;
Automata |
Published in: |
Publicacions matemàtiques, Vol. 66 Núm. 2 (2022) , p. 789-830 (Articles) , ISSN 2014-4350 |
Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/402264
DOI: 10.5565/PUBLMAT6622209
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Record created 2022-07-27, last modified 2024-02-09