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Dihedral group

Revision as of 13:24, 27 August 2020 by Duck master (talk | contribs) (created page)
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The dihedral groups $D_{2n}$ are an infinite family of groups which are in general noncommutative. Each dihedral group $D_{2n}$ is defined to be the group of linear symmetries of a regular $n$-gon.

Properties

  • The order of $D_{2n}$ is $2n$.
  • The group $D_{2n}$ has a presentation in the form $<r, s|r^n = 1, s^2 = 1, srs = r^{-1}>$.
  • For $n > 3$, $D_{2n}$ is noncommutative.

See also

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