Dihedral Group - Equivalent Definitions

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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