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oai:recercat.cat:2072/4525282024-06-06T09:45:03Zcom_2072_98col_2072_378195
RECERCAT author Burillo Puig, Josep author Cleary, Sean author Stein, Melanie author Taback, Jennifer author Centre de Recerca Matemàtica 2005 We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T. open access Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. https://creativecommons.org/licenses/by-nc-nd/2.5/ Grups, Teoria dels Combinatorial and metric properties of Thompson's group T Article Prepublicació