-
called the "semidihedral group".
Dummit and
Foote refer to it as the "
quasidihedral group"; we
adopt that name in this article. All give the same presentation...
-
cyclic groups is metacyclic.
These include the
dihedral groups and the
quasidihedral groups. The
dicyclic groups are metacyclic. (Note that a
dicyclic group...
-
includes both of the
examples above, as well as many
other groups. The
quasidihedral groups are
family of
finite groups with
similar properties to the dihedral...
-
other three 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...
- Nilpotent. 36 G168 QD16 Z8, Q8, D8, Z4 (3), Z22 (2), Z2 (5) The
order 16
quasidihedral group. Nilpotent. 37 G169 Q16 Z8, Q8 (2), Z4 (5), Z2
Generalized quaternion...
- 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...
-
product of an
extraspecial group with a
group that is cyclic, dihedral,
quasidihedral, or quaternion.
Gorenstein (1980, 5.4.9)
gives a
proof of this result...
- Alperin–Brauer–Gorenstein
theorem characterizes the
finite simple groups with
quasidihedral or
wreathed Sylow 2-subgroups.
These are
isomorphic either to three-dimensional...
- Alperin–Brauer–Gorenstein
theorem classified finite groups with
wreathed or
quasidihedral Sylow 2-subgroups. The
methods developed by
Brauer were also instrumental...
- G is
isoclinic with G×A if and only if A is abelian. The dihedral,
quasidihedral, and
quaternion groups of
order 2n are
isoclinic for n≥3, Berkovich...
