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On subgroups of R. Thompson's group $F$
Post-edited
Authors : Sapir, Mark (Author of the conference)
CIRM (Publisher )
20E07 - Subgroup theorems
20F05 - Generators, relations, and presentations of groups
20F65 - Geometric group theory
CIRM (Publisher )
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| Jones' subgroup Thompson group semigroup diagram Thompson group & links theorem about Jones' subgroup Savchuk's problem 2-core of a subgroup |
Abstract :
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 $H_i$.
MSC Codes : 20E07 - Subgroup theorems
20F05 - Generators, relations, and presentations of groups
20F65 - Geometric group theory
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Information on the Video
Film maker : Vichi, PascalLanguage : English Available date : 13/10/2015 Conference Date : 15/09/15 Subseries : Research talks arXiv category : Group Theory Mathematical Area(s) : Algebra Format : QuickTime (.mov) Video Time : 00:55:58 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-09-15_Sapir.mp4 
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Information on the Event
Event Title : GAGTA-9: geometric, asymptotic and combinatorial group theory and applications / GAGTA-9 : Théorie géométrique, asymptotique et combinatoire des groupes et applications Event Organizers : Coulbois, Thierry ; Weil, Pascal Dates : 14/09/15 - 18/09/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1212.html
Citation Data
DOI : 10.24350/CIRM.V.18836503Cite 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 |
Bibliography
- Golan, G., & Sapir, M. (2015). On subgroups of R. Thompson's group $F$.
- Golan, G., & Sapir, M. (2015). On Jones' subgroup of R. Thompson group $F$.
