Turkish Journal of Mathematics
DOI
10.3906/mat-2108-88
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$_{n}$).
Keywords
Coxeter group, generating set, generators, order
First Page
2623
Last Page
2645
Recommended Citation
HART, SARAH B.; KELSEY, VERONICA; and ROWLEY, PETER
(2021)
"Generating finite Coxeter groups with elements of the same order,"
Turkish Journal of Mathematics: Vol. 45:
No.
6, Article 17.
https://doi.org/10.3906/mat-2108-88
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss6/17
