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H 2 On subgroups of R. Thompson's group $F$

Auteurs : Sapir, Mark (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Jones' subgroup Thompson group semigroup diagram Thompson group & links theorem about Jones' subgroup Savchuk's problem 2-core of a subgroup

Résumé : We provide two ways to show that the R. Thompson group $F$ has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of $F$ on $(0,1)$, thus solving a problem by D. Savchuk. The first way employs Jones' subgroup of the R. Thompson group $F$ and leads to an explicit finitely generated example. The second way employs directed 2-complexes and 2-dimensional analogs of Stallings' core graphs, and gives many implicit examples. We also show that $F$ has a decreasing sequence of finitely generated subgroups $F>H_1>H_2>...$ such that $\cap H_i={1}$ and for every $i$ there exist only finitely many subgroups of $F$ containing $H_i$.

Codes MSC :
20E07 - Subgroup theorems
20F05 - Generators, relations, and presentations of groups
20F65 - Geometric group theory

 Informations sur la Vidéo Réalisateur : Vichi, Pascal Langue : Anglais Date de publication : 13/10/15 Date de captation : 15/09/15 Collection : Research talks ; Algebra Format : QuickTime (.mov) Durée : 00:55:58 Domaine : Algebra Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2015-09-15_Sapir.mp4 Informations sur la rencontre Nom de la rencontre : GAGTA-9: geometric, asymptotic and combinatorial group theory and applications / GAGTA-9 : Théorie géométrique, asymptotique et combinatoire des groupes et applications Organisateurs de la rencontre : Coulbois, Thierry ; Weil, PascalDates : 14/09/15 - 18/09/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1212.html Citation Data DOI : 10.24350/CIRM.V.18836503 Cite this video as: Sapir, Mark (2015). On subgroups of R. Thompson's group $F$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18836503 URI : http://dx.doi.org/10.24350/CIRM.V.18836503

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