Let and be groups, and let act on the set . Define the action of on the direct product by
Note that by definition of the action of on ,
The action of on in the semidirect product permutes the elements of a tuple , and the group operation defined on gives pointwise multiplication. To be explicit, suppose is an -tuple, and let . Let denote . Then
Notice the permutation of the indices in (*).
A bit amount of thought to understand this slightly messy notation will be illuminating, and might also shed some light on the choice of terminology.
|Date of creation||2014-12-30 11:23:20|
|Last modified on||2014-12-30 11:23:20|
|Last modified by||juanman (12619)|