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Research talks;Algebra

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 $H_i$. 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, ...

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Documents 20F05 | enregistrements trouvés : 49

On subgroups of R. Thompson's group $F$ Sapir, Mark | CIRM H Nouveau

Burnside groups :proceedings of a workshop held at the university of bielefeld#June-July Mennicke, J. L. | Springer-Verlag 1980 Nouveau

Asymptotic invariants of infinite groups, Volume 2geometric group theory proceedings of the symposium held in Sussex 1991 Gromov, M. | Cambridge University Press 1993 Nouveau

Geometric group theory. Vol. 1 :geometric group theory proceedings of the symposium held in Sussex 1991 Niblo, Graham A. ; Roller, Martin A. | Cambridge University Press 1993 Nouveau

Séminaire de géométrie algébrique du Bois Marie 1962-64 SGA 3structure des schémas en groupes réductifs III Artin, Michael ; Bertin, J. E. ; Demazure, M. ; Gabriel, P. ; Grothendieck, A. | Springer-Verlag 1970 Nouveau

Summer school in group theory :Third annual crm summer school#Aug. 11-23 Kharlampovich, Olga | American Mathematical Society 1999 Nouveau

Combinatorial group theory, discrete groups, and number theory :a conference in honor of Gerhard Rosenberger#Dec. 8-9AMS special session on infinite groups#Oct. 8-9 Fine, Benjamin ; Gaglione, Anthony ; Spellman, Denis | Amercian Mathematical Society 2006 Nouveau

Séminaire Bourbaki. Vol. 2012/2013: exposés 1059-1073 | Société Mathématique de France 2014 Nouveau

Hyperbolic geometry and geometric group theoryTokyo # July 30 - August 5, 2014 Fujiwara, Koji ; Kojima, Sadayoshi ; Ohshika, Ken'ichi | Mathematical Society of Japan 2017 Nouveau

The classification of excursions Mishna, Marni | CIRM H Nouveau

Combinatorial group theory :presentations of groups in terms of generators and relations Magnus, Wilhelm ; Karrass, Abraham ; Solitar, Donald | Interscience Publishers 1966 Nouveau

Théorie des groupes :cours d'initiation Dubreil, Paul | Dunod 1972 Nouveau

Generators and relations for discrete groups Coxeter, H. S. M. ; Moser, W. O. J. | Springer-Verlag 1965 Nouveau

Les groupes fondamentaux et les produits fondamentaux de groupes Piccard, Sophie | Publication du Centre de Recherches en Mathématiques Pures 1981 Nouveau

The history of combinatorial group theorya case study in the history of ideas Chandler, Bruce ; Magnus, Wilhelm | Springer-Verlag 1982 Nouveau

Lectures on Chevalley groups Steinberg, Robert | Yale University Department of mathematics 1967 Nouveau

Papers on group theory and topology Dehn, Max | Springer-Verlag 1987 Nouveau

Finite presentability of s-arithmetic groups compact presentability of solvable groups Abels, Herbert | Springer-Verlag 1987 Nouveau

Free group rings Gupta, Narian | American Mathematical Society 1987 Nouveau

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Burnside groups :
proceedings of a workshop held at the university of bielefeld#June-July Mennicke, J. L. | Springer-Verlag 1980 Nouveau

Asymptotic invariants of infinite groups, Volume 2
geometric group theory proceedings of the symposium held in Sussex 1991 Gromov, M. | Cambridge University Press 1993 Nouveau

Geometric group theory. Vol. 1 :
geometric group theory proceedings of the symposium held in Sussex 1991 Niblo, Graham A. ; Roller, Martin A. | Cambridge University Press 1993 Nouveau

Séminaire de géométrie algébrique du Bois Marie 1962-64 SGA 3
structure des schémas en groupes réductifs III Artin, Michael ; Bertin, J. E. ; Demazure, M. ; Gabriel, P. ; Grothendieck, A. | Springer-Verlag 1970 Nouveau

Summer school in group theory :
Third annual crm summer school#Aug. 11-23 Kharlampovich, Olga | American Mathematical Society 1999 Nouveau

Combinatorial group theory, discrete groups, and number theory :
a conference in honor of Gerhard Rosenberger#Dec. 8-9
AMS special session on infinite groups#Oct. 8-9 Fine, Benjamin ; Gaglione, Anthony ; Spellman, Denis | Amercian Mathematical Society 2006 Nouveau

Hyperbolic geometry and geometric group theory
Tokyo # July 30 - August 5, 2014 Fujiwara, Koji ; Kojima, Sadayoshi ; Ohshika, Ken'ichi | Mathematical Society of Japan 2017 Nouveau

Combinatorial group theory :
presentations of groups in terms of generators and relations Magnus, Wilhelm ; Karrass, Abraham ; Solitar, Donald | Interscience Publishers 1966 Nouveau

Théorie des groupes :
cours d'initiation Dubreil, Paul | Dunod 1972 Nouveau

The history of combinatorial group theory
a case study in the history of ideas Chandler, Bruce ; Magnus, Wilhelm | Springer-Verlag 1982 Nouveau