I have a theorem states that:

Let, and letand.Thenand.

Then I have this corollary:

If,then.

Please check for me if my proof for the corollary is correct.

Proof:

We consider,i.e. H has no proper normal subgroup..

Also,

By last theorem, .

We have.

Since H has no proper normal subgroup, so quotient group of H is not defined. Also,.

Hence,