On Minimal Generating Sets of Certain Subsemigroups of Isometries

Abstract

Let DPn and ODPn be the semigroups of all isometries and of all order-preserving isometries on Xn, respectively. In this paper we investigate the structure of minimal generating sets of the subsemigroup DPn,r = {α ∈ DPn : |im (α)| ≤ r} (similarly of the subsemigroup ODPn,r = {α ∈ ODPn : |im (α)| ≤ r}) for 2 ≤ r ≤ n − 1.