Wednesday, 25 April 2018

Timur Nasybullov: Twisted conjugacy classes in unitriangular groups

Let $\varphi$ be an automorphism of a group $G$. Two elements $x,y$ of $G$ are said to be $\varphi$-conjugated if there exists an element $z\in G$ such that $x=z^{-1}y\varphi(z)$. The relation of $\varphi$-conjugation is a natural generalization of the usual conjugation in a group.
In the talk we are going to discuss some properties of groups, involving twisted conjugacy classes: the $R_{\infty}$-property, dependence of the structure of a group from the number of twisted conjugacy classes, connections between properties of the twisted conjugacy class of the unit element and properties of a group.
We will make an accent on the recent results about $\varphi$-conjugacy classes in the group of unitriangular matrices.

• © 2012-2015 Universität Bielefeld
• Kontakt
• Impressum