Type: Seminar

Distribution: World

Expiry: 29 Oct 2009

Auth: claus@109.104.233.220.static.exetel.com.au (fcla9404) in SMS-WASM

In 1939, Coxeter first studied the family of groups defined by the presentations: (l,m,n;q) = < r, s | r^l, s^m, (rs)^n,[r,s]^q >. Until recently, the finiteness of only 6 of these groups remained undecided: (2, 3, 13; 4), (3, 4, 9; 2), (3, 4, 11; 2), (3, 4, 13; 2), (3, 5, 6; 2) and (3, 5, 7; 2). We discuss a recent computational proof, carried out largely in Magma, by George Havas and myself that (2, 3, 13; 4) is finite, and that (3, 4, 13; 2) and (3, 5, 7; 2) are infinite.