Abstract

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps and those maps that are expressible as a composite of three involutions are determined in the isometry groups of spherical, Euclidean and hyperbolic space in several dimensions.