Onto extensions of free groups
Rationale Cocaine addiction is a chronic relapsing disorder that lacks of an effective treatment. Isoflavones are a family of compounds present in different plants and vegetables like soybeans that share a common chemical structure. Previous studies have described that synthetic derivatives from the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/365270 |
| Acceso en línea: | https://hdl.handle.net/2117/365270 https://dx.doi.org/10.46298/jgcc.2021.13.1.7036 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Free group Subgroup extension Onto extension Algebraic extension Stallings graph Grups infinits Grups finits Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | Rationale Cocaine addiction is a chronic relapsing disorder that lacks of an effective treatment. Isoflavones are a family of compounds present in different plants and vegetables like soybeans that share a common chemical structure. Previous studies have described that synthetic derivatives from the natural isoflavone daidzin can modulate cocaine addiction, by a mechanism suggested to involve aldehyde-dehydrogenase (ALDH) activities. An extension of subgroups H 6 K 6 FA of the free group of rank |A| = r > 2 is called onto when, for every ambient basis A 0 , the Stallings graph GA0 (K) is a quotient of GA0 (H). Algebraic extensions are onto and the converse implication was conjectured by Miasnikov–Ventura–Weil, and resolved in the negative, first by Parzanchevski–Puder for rank r = 2, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion –into extensions– becomes trivial, making a Takahasi type theorem not possible in this setting. |
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