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Título:	Intersection problem for Droms RAAGs
Autor/a:	Delgado Rodríguez, Jorge; Ventura Capell, Enric; Zakharov, Alexander
Otros autores:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
Abstract:	We solve the subgroup intersection problem (SIP) for any RAAG G of Droms type (i.e., with defining graph not containing induced squares or paths of length 3): there is an algorithm which, given finite sets of generators for two subgroups H,K of G, decides whether HnK is finitely generated or not, and, in the affirmative case, it computes a set of generators for HnK. Taking advantage of the recursive characterization of Droms groups, the proof consists in separately showing that the solvability of SIP passes through free products, and through direct products with free-abelian groups. We note that most of RAAGs are not Howson, and many (e.g. F_2 x F_2) even have unsolvable SIP.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups -Group theory -Finite groups -Partially commutative group -right-angled Artin group -Droms group -Intersection problem -Finite generation -Free product -Direct product -Grups, Teoria de -Grups finits -Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups -Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
Derechos:	Attribution 3.0 Spain http://creativecommons.org/licenses/by/3.0/es/
Tipo de documento:	Artículo - Borrador Artículo
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