Difference between revisions of "Dihedral group"
From Encyclopedia of Mathematics
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| − | A group isomorphic to the rotation group of a dihedron, i.e. of a regular doubled [[Pyramid|pyramid]]. If the base of the pyramid is an | + | A group isomorphic to the rotation group of a dihedron, i.e. of a regular doubled [[Pyramid|pyramid]]. If the base of the pyramid is an $n$-gon, the corresponding dihedron group is of order $2n$ and is generated by two rotations $\phi$ and $\psi$ of orders $n$ and $2$ respectively, with the defining relation $\phi\psi\phi\psi=1$. 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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> G.G. Hall, "Applied group theory" , Longman (1967)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> G.G. Hall, "Applied group theory" , Longman (1967)</TD></TR></table> | ||
Revision as of 14:11, 17 July 2014
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 $n$-gon, the corresponding dihedron group is of order $2n$ and is generated by two rotations $\phi$ and $\psi$ of orders $n$ and $2$ respectively, with the defining relation $\phi\psi\phi\psi=1$. 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=32459
Dihedral group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dihedral_group&oldid=32459
This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article