Difference between revisions of "Dihedral group"
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* The [[order (group theory)|order]] of <math>D_{2n}</math> is <math>2n</math>. | * The [[order (group theory)|order]] of <math>D_{2n}</math> is <math>2n</math>. | ||
| − | * The group <math>D_{2n}</math> has a [[presentation]] in the form <math> | + | * The group <math>D_{2n}</math> has a [[presentation]] in the form <math>\langle r, s\mid r^n = 1, s^2 = 1, srs = r^{-1}\rangle</math>. |
* For <math>n > 3</math>, <math>D_{2n}</math> is noncommutative. | * For <math>n > 3</math>, <math>D_{2n}</math> is noncommutative. | ||
Latest revision as of 09:17, 11 March 2024
The dihedral groups 
are an infinite family of groups which are in general noncommutative. Each dihedral group is defined to be the group of linear symmetries of a regular 
-gon.
Properties
- The order of
is 
. - The group has a presentation in the form
. - For
, is noncommutative.
.
.
, See also
- Symmetric group
- Cyclic group
- RotationThis article is a stub. Help us out by expanding it.
