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

Famous quotes containing the words equivalent and/or definitions:

    “Divorce is the psychological equivalent of a triple coronary bypass.”
    —Mary Kay Blakely (20th century)

    “What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
    —G.C. (Georg Christoph)