Generating finite Coxeter groups with elements of the same order

Abstract

Supposing G is a group and k a natural number, d_k(G) is defined to be the minimal number of elements of G of order k which generate G (setting d_k(G)=0 if G has no such generating sets). This paper investigates d_k(G) when G is a finite Coxeter group either of type B_n or D_n, or of exceptional type. Together with work of Garzoni and Yu, this determines d_k(G) for all finite irreducible Coxeter groups G when k is between 2 and rank(G) (or rank(G)+1 when G is of type A_n).