Hi,

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.