On commutator and power subgroups of some coxeter groups

Abstract

In this paper the commutator subgroups of the affine Weyl group of type Cn-1 (n ≥ 3) and the triangle Coxeter groups are studied. Also it is given all power subgroups of the affine Weyl group of type Ãn-1 (n ≥ 3). We should note that, as in our knowledge, although the concept of this study seems in pure mathematics, it is known that affine Weyl groups have a direct relationship between discrete dynamical systems and Painlevé equations (cf. [16]).