Subgroup majorization

The extension of majorization (also called the rearrangement ordering), to more general groups than the symmetric (permutation) group, is referred to as G-majorization. There are strong results in the case that G is a reflection group and this paper builds on this theory in the direction of subgroups, normal subgroups, quotient groups and extensions. The implications for fundamental cones and order-preserving functions are studied. The main example considered is the hyperoctahedral group, which, acting on a vector in Rn, permutes and changes the signs of components.