Twisted conjugacy in Richard Thompson's group T

Daciberg L. Gonçalves; Parameswaran Sankaran

Twisted conjugacy in Richard Thompson's group T

Group Theory 2013-12-10 v2

Authors: Daciberg L. Gonçalves , Parameswaran Sankaran

Abstract

Let $f$ be an automorphism of a group $G$ . Two elements $x, y$ in $G$ are said to be in the same $f$ -twisted conjugacy class if there exists an element $z$ in $G$ such that $y=z x f(z^{-1})$ . This is an equivalence relation known as $f$ -twisted conjugacy. If the number $R(f)$ of $f$ -twisted conjugacy classes is infinite for every automorphism $f$ of $G$ one says that $G$ has the $R_\infty$ -property. We show that the Richard Thompson group $T$ has the $R_\infty$ -property.

Keywords

twisted conjugacy Richard Thompson's group T R∞-property automorphism

Cite

@article{arxiv.1309.2875,
  title  = {Twisted conjugacy in Richard Thompson's group T},
  author = {Daciberg L. Gonçalves and Parameswaran Sankaran},
  journal= {arXiv preprint arXiv:1309.2875},
  year   = {2013}
}

Comments

Nine pages, no figures. There was an error in the statement of Theorem 2.1 which is corrected. A new reference has been added

Twisted conjugacy in Richard Thompson's group T

Abstract

Keywords

Cite

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