Problem: - simple has subgroups of order and we could embedding it into .
Solution: First part is easy to show from Sylow Theorem.
Suppose that we have - Sylow -subgroups and consider following mapping:
, and .
is homomorphism (it is easy to show that )
<--- may I describe kernel such that? If yes then:
or - because is simple.
If , then , so are simple - bad choice.
So then is monomorphis. [qed]
Is this solution good? Thanks for any advices.