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