Corpus ID: 119642551

An Irrational-slope Thompson's Group

@article{Burillo2018AnIT,
  title={An Irrational-slope Thompson's Group},
  author={J. Burillo and B. Nucinkis and Lawrence Reeves},
  journal={arXiv: Group Theory},
  year={2018}
}
The purpose of this paper is to study the properties of the irrational-slope Thompson's group $F_\tau$ introduced by Cleary in 1995. We construct presentations, both finite and infinite and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary… Expand
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