Twisted conjugacy in Richard Thompson's group T

arXiv1309.2875MaRDI QIDQ6244725

Parameswaran Sankaran, Daciberg Lima Gonçalves

Publication date: 11 September 2013

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 $y=zxf(z^{-1})$. 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 $R_{i}nfty$-property. We show that the Richard Thompson group $T$ has the $R_{i}nfty$-property.

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Automorphisms of infinite groups (20E36)

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