These are some random examples of groups:
 * Continuous groups
  1. Z,+ 	infinite abelian
  2. Z,*  not a group.  violates inverse
  3. R,*  not a group.  violates inverse for 0
  4. R,+  infinite abelian
  5. R*=R-{0},* infinite abelian
  6. R*=R-{0},+ not a group.  violates identity
 * Finite groups
   1. {e}  order 1
   2. cyclic group
   3. dihedral group
   4. Z mod n,+
 * Conjugacy classes