For anyone who has John Fraleigh "A First Course in Abstract Algebra" 7/e would be easier to follow. (I definitely know some of you have it, because many people referred to it already, very popular book).

Let

be a prime.

On Page, 324-325

John is talking about the first Sylow theorem.

"Given a finite group

with

and

, then there exists a subgroup of order

for

.

Furthermore, each subgroup of order

is a normal subgroup of order

. For

.

----

The first part of the proof I understand, the second part ails my soul and makes my blood cold and so by degrees.

I believe that John wanted to write,

is a normal subgroup of

**some** group of order

. He makes it appear as though it is true for all subgroups, which is unlikely.

Anyone know what I am talking about?