Problemas de conjugación en los grupos de Thompson

The conjugacy problem asks if, given a finitely generated group G with generating set S, it is possible to decide whether two given words are conjugated elements of G. That is, given two words w1, w2 in the S alphabet, representing the group elements g and h, respectively, can we decide if there is z ∈ G such that g = zhz−1?

There are a number of variations of this problem, such as the twisted and power conjugacy problems, and some results concerning them can be obtained for the Thompson’s and Higman-Thompson’s groups.

In this talk we will define the Thompson’s groups F, T and V , giving some of their main properties and results on their conjugacy problems. After that, we will construct the Higman-Thompson groups, which can be viewed as a generalization of the first three groups. Again, we will state some of the main properties and results about their conjugacy problems.