Dihedral Group - Generalizations

Generalizations

There are several important generalizations of the dihedral groups:

• The infinite dihedral group is an infinite group with algebraic structure similar to the finite dihedral groups. It can be viewed as the group of symmetries of the integers.
• The orthogonal group O(2), i.e. the symmetry group of the circle, also has similar properties to the dihedral groups.
• The family of generalized dihedral groups includes both of the examples above, as well as many other groups.
• The quasidihedral groups are family of finite groups with similar properties to the dihedral groups.