 The ends of a finitely generated group are defined to be the ends of the corresponding Cayley graph; this definition is insensitive to the choice of generating set.Every finitely-generated infinite group has either 1, 2, or infinitely many ends, and Stallings theorem about ends of groups provides a decomposition for groups with more than one end.For a path connected CW-complex, the ends can be characterized as homotopy classes of proper maps formula_11, called rays in "X"