Computing Word Length in Alternate Presentations of Thompson's Group F
نویسندگان
چکیده
We introduce a new method for computing the word length of an element of Thompson’s group F with respect to a “consecutive” generating set of the form Xn = {x0, x1, · · · , xn}, which is a subset of the standard infinite generating set for F . We use this method to show that (F, Xn) is not almost convex, and has pockets of increasing, though bounded, depth dependent on n.
منابع مشابه
The Ubiquity of Thompson's Group F in Groups of Piecewise Linear Homeomorphisms of the Unit Interval1
In the 1960s, Richard J. Thompson introduced a triple of groups F T G which, among them, supplied: the rst examples of innnite, nitely presented, simple groups 14] (see 6] for published details); a technique for constructing an elementary example of a nitely presented group with an unsolvable word problem 12]; the universal obstruction to a problem in homotopy theory 8]; the rst examples of tor...
متن کاملMetric Properties of the Braided Thompson’s Groups
Braided Thompson’s groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups Bn, the finitary braid group B∞ and Thompson’s group F as subgroups. We describe some of the metric properties of braided Thompson’s groups and give upper and lower bounds for word length in terms of the number of strands and the number of crossings in the diagrams use...
متن کاملGeometric quasi-isometric embeddings into Thompson's group F
We use geometric techniques to investigate several examples of quasi-isometrically embedded subgroups of Thompson’s group F . Many of these are explored using the metric properties of the shift map φ in F . These subgroups have simple geometric but complicated algebraic descriptions. We present them to illustrate the intricate geometry of Thompson’s group F as well as the interplay between its ...
متن کاملNew characterization of some linear groups
There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...
متن کاملThe Automorphism Group of Thompson’s Group F : Subgroups and Metric Properties
We describe some of the geometric properties of the automorphism group Aut(F ) of Thompson’s group F . We give realizations of Aut(F ) geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective methods for estimating the word length of elements. We study some natural subgroups of Aut(F ) and their metric properties. In particular, we show that the subg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJAC
دوره 19 شماره
صفحات -
تاریخ انتشار 2009