Mathematics Colloquium
Thursday, November 12, 2009
Kerchof Hall 317, 4:00 pm
Refreshments served at 3:30 pm in the lounge
Title: Presentations of Symmetric Groups (joint work with R. Guralnick, W. Kantor, A. Lubotzky )
Abstract: We study presentations of symmetric groups Sym(n) from a
quantitative point of view. Our main result provides somewhat
unexpected answers to the following questions: how many relations
are needed to define Sym(n), and how short can these relations be?
I will describe the main idea which allows us to produce presentations with a
bounded number of relations (independent on n). I will also explain several
tricks which further allow us to shorten the lengths of the relations
and decrease their number to less than 10.