Automorphisms and products of ordered sets
An ordered set X has the fixed point property if every order preserving map of X to X has a fixed point. The paper deals with the following problem: if ordered sets X and Y have the fixed point property, does it follow that the (cardinal) product XY has the fixed point property. The main result is the following. Let X and Y be both either finite connected ordered sets or connected ordered sets, each with a decomposition as a product of product indecomposable ordered sets. Then XY has a fixed point free automorphism if and only if at least one of X and Y has a fixed point free automorphism.
product of product indecomposable ordered sets
scientific article; zbMATH DE number 3882493