Texas A&M University, Department of
Mathematics, 216 Milner Hall, 16th of February 2005, 3:00-3:50
Groups and Dynamics Seminar
Magnus embeddings
and branch groups
Said Sidki of Universidade de
Brasília,
Brazil
Given a group P and a generating set X, we construct a tree indexed by
the free monoid freely generated by the symbols from P, and make P act
on it by the regular representation. For each generator in X we
construct an automorphism of the tree, in a manner similar to the
Magnus embedding; these generators are automorphisms of bounded growth.
If P satisfies some mild conditions, the group G(P,X) generated by
these automorphisms will be shown to be weakly branch with many
additional properties.