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:

    “Accountability in friendship is the equivalent of love without strategy.”
    —Anita Brookner (b. 1938)

    “The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
    —Pamela Patrick Novotny (20th century)