Texas A&M University, Department of
Mathematics, 216 Milner Hall, 18th of October 2006, 3:00-3:50
Groups and Dynamics Seminar
Virtual
endomorphisms of groups
Said Sidki of Universidade de
Brasília,
Brazil
Given a group G with a subgroup H of finite index m, a homomorphism f:
H -> G is called a virtual endomorphism of G. The representation of
G on the right cosets of H extends, with the use of f, to a
representation t of G into the group of automorphisms of a 1-rooted m-ary tree. The
kernel of t is the largest subgroup L of H which is normal in G and is
f-invariant. The image of t is a state-closed (or, self-similar) group.
The class of finitely generated state-closed groups includesimportant
examples such as those studied by Grigorchuk, Nekrachevych, Sunik,
Vorobets and other mathematicians. We will talk aboutalgebraic
developments in this area, with special emphasis on torsion-free
nilpotent groups