Group theory and generalizations Proposition

Order of the dihedral group

Builds on Dihedral group Order of a group

Statement

Let $n \geq 3$ . The dihedral group $D_n$ has order $2n$ .

Remarks

A symmetry of the regular $n$ -gon is determined by the image of one vertex and by whether it keeps or reverses the orientation. There are $n$ choices for the image of the vertex and $2$ choices for the orientation. For example, $D_3$ has order $6$ and $D_4$ has order $8$ .

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Group concept
Symmetry group concept
Order of a group definition
Subgroup definition
Subgroup criterion statement
Intersection of subgroups is a subgroup statement
Subgroup generated by a subset definition
Dihedral group definition
Order of the dihedral group statement

Tag	`0BZVNWJ352`
URI	`m2://0BZVNWJ352`
Kind	statement, proposition
Writing	W0 stub
MSC	20B25
Status	This copy of the site has no build data. Run `m2 status 0BZVNWJ352`.
Uses	Dihedral group, Order of a group

Order of the dihedral group

Statement

Remarks

Reading path

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