21. The homography group on this projective line has 12 elements, also described with matrices or as permutations. 22. Examples include the real projective line , the complex projective line, and the projective line over quaternions. 23. Examples include the real projective line, the complex projective line , and the projective line over quaternions. 24. Examples include the real projective line, the complex projective line, and the projective line over quaternions. 25. The quaternionic projective line \ mathbb { HP } ^ 1 is homeomorphic to the 4-sphere. 26. In the study of collineations, the case of projective lines is special due to the small dimension. 27. Since the center acts trivially, the projective linear group,, also acts on the projective line . 28. For the spacetime conformal group, it is sufficient to consider homographies on the projective line over that ring. 29. The projective line over the real numbers is called the "'real projective line " '. 30. The projective line over the real numbers is called the "'real projective line " '.
