examples of semidirect products of groups
Suppose and let be a generator for . Let . Define by . Let . Then in ,
by the canonical equivalence of inner and outer semidirect products. So has elements, two generators satisfying
and thus , the dihedral group.
If instead , the result is the infinite dihedral group.
As another example, if is a group, then the holomorph of is under the identity map from to itself.
|Title||examples of semidirect products of groups|
|Date of creation||2013-03-22 17:22:52|
|Last modified on||2013-03-22 17:22:52|
|Last modified by||rm50 (10146)|