Vorträge in der Woche 18.06.2007 bis 24.06.2007

Montag, 18.06.2007: Short presentations for symmetric and classical groups

Prof. Dr. Marston Conder

The classical presentation for the symmetric group S n is given in terms of transpositions t i (i,i 1) for 1 le i n and the Coxeter relations satisfied by these. Note that the number of generators is linear and the number of relations is quadratic in n . I will describe some new presentations for S n that involve a fixed number of generators and relations, and how these can be used to obtain short presentations for the alternating groups A n and also for the classical linear groups. This is joint work with John Bray, Charles Leedham-Green and Eamonn O'Brien.