Combinatorial properties of Thompson’s group 𝐹

DOI10.1090/S0002-9947-03-03375-0zbMath1065.20052arXivmath/0208117OpenAlexW1493625369MaRDI QIDQ4813787

Sean Cleary, Jennifer Taback

Publication date: 13 August 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208117

zbMATH Keywords

presentationsnormal formsCayley graphsword lengthsThompson group \(F\)dead endstree pair diagramsdeep pocketstypes of carets

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items

BOUNDING RIGHT-ARM ROTATION DISTANCES, The automorphism group of Thompson's group \(F\): subgroups and metric properties., Thompson's group \(F\) and the linear group \(\mathrm{GL}_\infty(\mathbb Z)\)., Strict Dead-End Elements in Free Soluble Groups, FACTORIZATIONS OF THE THOMPSON–HIGMAN GROUPS, AND CIRCUIT COMPLEXITY, Tame combing and almost convexity conditions., A finitely presented group with unbounded dead-end depth, Frobenius problem and dead ends in integers, Distortion of wreath products in Thompson's group \(F\)., Unusual geodesics in generalizations of Thompson's group \(F\)., Counting elements and geodesics in Thompson's group \(F\)., Combinatorial and metric properties of Thompson’s group 𝑇, Cone types and geodesic languages for lamplighter groups and Thompson's group \(F\)., FOREST DIAGRAMS FOR ELEMENTS OF THOMPSON'S GROUP F, SOME REMARKS ON DEPTH OF DEAD ENDS IN GROUPS, Bounding restricted rotation distance, COMPUTING WORD LENGTH IN ALTERNATE PRESENTATIONS OF THOMPSON'S GROUP F, THE UNBOUNDED DEAD-END DEPTH PROPERTY IS NOT A GROUP INVARIANT, Random subgroups of Thompson's group \(F\).

Cites Work

• An infinite-dimensional torsion-free \(\text{FP}_{\infty}\) group
• Quasi-isometrically embedded subgroups of Thompson's group \(F\)
• Introductory notes on Richard Thompson's groups
• Minimal length elements of Thompson's group \(F\)
• Thompson's group \(F\) is not almost convex.
• Metrics and embeddings of generalizations of Thompson’s group $F$