Hi everyone,
I am reading the book "Hyperbolic Geometry from a Local Viewpoint" by Linda Keen and Nikola Lakic.

My question is about side-paired fundamental polygon.

On page 108, there is a note that says: "In the rest of this chapter we will reserve the notation A for side pairing elements of the group. Other elements will be denoted by other letters. In particular, elements that are products of side pairing elements, that is, words in the side pairing elements, will be denoted by W."

If a and b are to elements and their product is ab, then ab is a word.
Is there any other reason to call ab a word else that it is a and b are two letters?