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 the work of Garzoni and Yu, 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 ).