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.