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?