A class of subgroups of Thompson’s group V

نویسندگان

  • Mark V. Lawson
  • Patrick Dehornoy
چکیده

We prove that the subgroups of the Thompson group V which are closed under a binary operation introduced by K. S. Brown are in bijective correspondence with a class of varieties of algebras with a single binary operation. In addition, we prove that there are exactly three such proper subgroups which contain the Thompson group F . 2000 AMS Subject Classification: 20F05, 20M18.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A dynamical definition of f.g. virtually free groups

We show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson’s group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0, 1}. There are also connections with formal language theory, as the class of gr...

متن کامل

Free Products in R. Thompson’s Group V

We investigate some product structures in R. Thompson’s group V , primarily by studying the topological dynamics associated with V ’s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two gen...

متن کامل

Pure Braid Subgroups of Braided Thompson’s Groups

We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...

متن کامل

Square roots of Thompson’s group F

We study two–generated subgroups x f , gy Homeo pIq such that x f 2, g2y is isomorphic to Thompson’s group F. We show that this class contains examples with nonabelian free subgroups, examples which do not admit faithful actions by C diffeomorphisms on 1–manifolds, and examples which are not finitely presented. We thus answer questions due to M. Brin.

متن کامل

Finiteness Properties of Some Groups of Local Similarities

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson’s group V . Guided by previous work on Thompson’s group V , we establish a number of new results about FSS groups. Our main result is that a class of FSS groups are of type F∞. This generalizes ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007