Quasi-dihedral group

From Encyclopedia of Mathematics
Revision as of 09:07, 19 October 2014 by Richard Pinch (talk | contribs) (link)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A finite $2$-group defined by generators $x,y$ and defining relations


where $m\geq4$. The order of a quasi-dihedral group is $2^m$; the group has a cyclic invariant subgroup of index 2. The name was given because of the similarity of the defining relations with those of a dihedral group; however, a quasi-dihedral group is not isomorphic to the latter for any value of $m$. A quasi-dihedral group is sometimes called a semi-dihedral group.


[1] B. Huppert, "Endliche Gruppen" , 1 , Springer (1967)
How to Cite This Entry:
Quasi-dihedral group. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by N.N. Vil'yams (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article