Stallings automata for free-times-abelian groups : intersections and index
Delgado Rodríguez, Jordi (Universidad del País Vasco. Departamento de Matemáticas)
Ventura, Enric (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.
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

42 p, 690.7 KB

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