In wikipedia article https://en.wikipedia.org/wiki/Translation_(geometry) it is written:
A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections.
Knowing that a glide reflection is just a composition of a reflection with a translation, I ask why citing this composition and not the other compositions like the composition of a translation and rotation or a composition of rotation and reflection ? what is special about the composition of a reflection and a translation that makes it one of the four rigid motions but not the other compositions ? Thank you for your help!
Because a composition between a translation and a rotation is already listed there, since such a composition is a rotation (typically with a different center). And a composition of a rotation and a reflection is another reflection. In other words, the list given is complete: every isometry is one of the things in that list, not just a composition of things in that list.