Generating Finite Coxeter Groups with Elements of the Same Order

Abstract

Supposing G is a group and k a natural number, dk(G) is defined to be the minimal number of elements of G of order k which generate G (setting dk(G)=0 if G has no such generating sets). This paper investigates dk(G) when G is a finite Coxeter group either of type Bn or Dn or of exceptional type. Together with Garzoni [3] and Yu [10], this determines dk(G) for all finite irreducible Coxeter groups G when 2≤k≤rank(G) (rank(G)+1 when G is of type An).