The series
The group
is the group generated by a rotation of angle
around a fixed axis D, and a symmetry on a plane P orthogonal to D.
Features
- Algebraic structure: it is Dihedral group of order 2m
- Kind of elements
- 1 element: identity,
- m-1 elements: rotation of angle k
with 1<=k<=m-1 around D,
- 1 element: plane symmetry on P,
- m-1 elements: plane symmetry on P composed with rotation of angle k
with 1<=k<=m-1 around D
- Particular cases
- if m=1, then the group is
- It has inversion if and only if n is even
- Examples