Texas A&M University, Department of
Mathematics, 216 Milner Hall, 12th of April 2006, 3:00-3:50
Groups and Dynamics Seminar
Almost
normal subgroups of SL(n, Z)
George Willis of University of Newcastle
The Margulis Normal Subgroup Theorem implies that, when n>2, any
normal subgroup of SL(n, Z) not contained in the centre has finite
index. In 1987, T. N. Venkataramana showed that the same conclusion
holds for subgroups that are almost normal,
that is, that are commensurable with all of their conjugates. The
argument of Venkataramana relies on techniques from the theory of
arithmetic groups.
Ideas for a new proof that derives Venkataramana’s result from that of
Margulis will be presented in the talk. The principal ingredients are
techniques from the structure theory of totally disconnected groups and
the notion of bounded generation of SL(n, Z). This is joint work
with Yehuda Shalom.