Equivalent Definitions
Further equivalent definitions of Dihn are:
- The automorphism group of the graph consisting only of a cycle with n vertices (if n ≥ 3).
- The group with presentation
-
- or
- From the second presentation follows that Dihn belongs to the class of Coxeter groups.
- The semidirect product of cyclic groups Zn and Z2, with Z2 acting on Zn by inversion (thus, Dihn always has a normal subgroup isomorphic to the group Zn
is isomorphic to Dihn if is the identity and is inversion.
Read more about this topic: Dihedral Group
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