- Construct every semidirect product of with itself.
- Show that (where denotes semidirect product).
- (G) Assume that is cyclic, is arbitrary and and are homomorphisms from into such that and are conjugate subgroups of Show that .
- Let be a -group of order for some . Show that for all ,
- Classify all groups of order:
- (G) 18.
- Find all abelian groups of order 2160.
- Give an example of a finite nonabelian group that cannot be written as a semidirect product of two of its proper subgroups.
- (G) Classify all groups of order for any prime