Word metric
In group theory, a word metric on a discrete group G {\displaystyle G} is a way to measure distance between any two elements of G {\displaystyle G} . As the name suggests, the word metric is a metric on G {\displaystyle G} , assigning to any two elements g {\displaystyle g} , h {\displaystyle h} of G {\displaystyle G} a distance d ( g , h ) {\displaystyle d(g,h)} that measures how efficiently their difference g − 1 h {\displaystyle g^{-1}h} can be expressed as a word whose letters come from a generating set for the group.