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
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