
please check for me
I have a theorem states that:
Let , and let and . Then and .
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,

Quote:
Originally Posted by
deniselim17 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,
It is correct except for a phrase you use "H has no proper normal subgroup", why not?
It does not matter. Just choose . We really do not care if it has proper normal subgroup (by the way it does, it has ) and then apply the theorem and get your result. But then you say something that is again not necessary "so the quotient group of H is not defined", yes it is! Certainly with . It is defined, it is just not a very interesting group.