Turkish Journal of Mathematics
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 the work of Garzoni and Yu, this determines $d_k(G)$ for all finite irreducible Coxeter groups $G$ when $2 \leq k \leq (G)$ ($(G)+1$ when $G$ is of type A$_{n}$).
DOI
10.3906/mat-2108-88
Keywords
Coxeter group, generating set, generators, order
First Page
2623
Last Page
2645
Recommended Citation
HART, S. B, KELSEY, V, & ROWLEY, P (2021). Generating finite Coxeter groups with elements of the same order. Turkish Journal of Mathematics 45 (6): 2623-2645. https://doi.org/10.3906/mat-2108-88
