# Dihedral group

From Encyclopedia of Mathematics

*dihedral group*

A group isomorphic to the rotation group of a dihedron, i.e. of a regular doubled pyramid. If the base of the pyramid is an -gon, the corresponding dihedron group is of order and is generated by two rotations and of orders and respectively, with the defining relation . A dihedral group is sometimes understood to denote the dihedral group of order 8 only. Two different elements of order 2 in any finite group generate a dihedral group.

#### References

[1] | G.G. Hall, "Applied group theory" , Longman (1967) |

**How to Cite This Entry:**

Dihedral group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dihedral_group&oldid=14889

This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article