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Foote refer to it as the "quasidihedral group"; we adopt that name in this article. All give the same presentation for this group: ⟨ r , s ∣ r 2 n − 1 =...

mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order n is 1, 1, 1, 2,...

dihedral groups. The family of generalized dihedral groups includes both of the examples above, as well as many other groups. The quasidihedral groups are...

are non-abelian groups: the dihedral group of order 16 the quasidihedral group of order 16 the Iwasawa group of order 16 If a given group is a semidirect...

the quasidihedral groups. The dicyclic groups are metacyclic. (Note that a dicyclic group is not necessarily a semidirect product of two cyclic groups.)...

simple groups with quasidihedral or wreathed Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective...

2-rank 2. Alperin showed that the Sylow subgroup must be dihedral, quasidihedral, wreathed, or a Sylow 2-subgroup of U3(4). The first case was done by...

an abelian group if and only if it is itself abelian, and G is isoclinic with G×A if and only if A is abelian. The dihedral, quasidihedral, and quaternion...

are all a central product of an extraspecial group with a group that is cyclic, dihedral, quasidihedral, or quaternion. Gorenstein (1980, 5.4.9) gives...

Alperin–Brauer–Gorenstein theorem classified finite groups with wreathed or quasidihedral Sylow 2-subgroups. The methods developed by Brauer were also instrumental...