Semidirect product decomposition of Coxeter groups

Cédric Bonnafé (1) , Matthew J. Dyer (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 DM-Notre Dame - Department of Mathematics

Let $(W,S)$ be a Coxeter system, let $S=I \dot{\cup} J$ be a partition of $S$ such that no element of $I$ is conjugate to an element of $J$, let $\widetilde{J}$ be the set of $W_I$-conjugates of elements of $J$ and let $\widetilde{W}$ be the subgroup of $W$ generated by $\widetilde{J}$. We show that $W=\widetilde{W} \rtimes W_I$ and that $(\widetilde{W},\widetilde{J})$ is a Coxeter system.

Mots clés: Coxeter groups; semidirect product

Domaines: Théorie des groupes [math.GR]

Cédric Bonnafé, Matthew J. Dyer. Semidirect product decomposition of Coxeter groups. 2008. ⟨hal-00282284v3⟩