Example in A Free Group
Suppose that F is the free group on the two element set . A word w in the symmetric generating set is said to be reduced if the letters do not occur next to each other in w, nor do the letters . Every element is represented by a unique reduced word, and this reduced word is the shortest word representing g. For example, since the word is reduced and has length 2, the word norm of equals 2, so the distance in the word norm between and equals 2. This can be visualized in terms of the Cayley graph, where the shortest path between b and a has length 2.
Read more about this topic: Word Metric
Famous quotes containing the words free and/or group:
“A great many will find fault in the resolution that the negro shall be free and equal, because our equal not every human being can be; but free every human being has a right to be. He can only be equal in his rights.”
—Mrs. Chalkstone, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 2, ch. 16, by Elizabeth Cady Stanton, Susan B. Anthony, and Matilda Joslyn Gage (1882)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)