Quasi-dihedral group

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A finite -group defined by generators and defining relations

where . The order of a quasi-dihedral group is ; 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 dihedron group; however, a quasi-dihedral group is not isomorphic to the latter for any value of . 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