Group (mathematics)/Catalogs

Most examples of groups come from considering some object and a set of bijective functions from the object to itself, which preserve some structure that this object has.

• Topological groups:
  • Matrix groups; e.g the general linear group, the special linear group, the projective linear group and the Platonic groups
  • Abelian varieties.
    • Elliptic curves.
    • Abelian surfaces.
• Finite groups.
  • Cyclic groups.
  • Symmetric groups and alternating groups.
  • Dihedral groups.
  • Group of quarternions.
• Galois groups.
• Fundamental groups.