# Jerusalem Mathematics Colloquium

Thursday, 25th October 2007, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Alex Lubotzky

(Hebrew University)

"Short presentations of finite simple groups"

** Abstract: **

Finding 'nice & compact' presentations of various groups has
been a subject of great interest for groups theorists for more than a
century. Well known presentations are the Coxeter presentation of the
finite symmetric groups and Steinberg presentation of groups of Lie type.
In respond to conjectures of Babai and Szemeredi on one hand (motivated
by questions in computational group theory) and of Mann on the other hand
(motivated by questions on subgroup growth) we show that all non-abelian
finite simple groups (with the possible exception of Ree groups) have
presentations which are small (bounded number of relations|) and short
(w.r.t the length of the relations). This is very suprising as the simple
abelian groups- the cyclic groups of prime order- do not have such
presentations!
We will describe the motivations and results, a cohomological
application (proving a conjecture of Holt) and some connections with
discrete subgroups of Lie groups and topology.

Joint work with Bob Guralnick, Bill Kantor and Martin Kassabov.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2007-08

Archive of talks