Books on Group Theory.

Question

I am looking for a book/note that has a good collection of advance results,theorems on finite group theory.

By advance, I mean theorems after Sylow,Lagranges(I am considering theorems of Sylow,Lagrange as basic which are available in any text of group theory).

Answer 1

I think one of the best and most complete book I know on (especially finite) group theory is Antonio Machì's http://www.springer.com/us/book/9788847024205 (original language: italian), despite the word "Introduction" in the subtitle.

The author is also the translator of Herstein's much more elementary $\textit{Algebra}$.

There are also many exercises and explained examples. Chapter $1$ is elementary, chapter 2 and 3 introduce also some interesting and often advanced techniques, and the remaining chapter are mostly advanced (i.e., you won't see those results in a basic six-months course along with Sylow and Lagrange).

Answer 2

I recommend you "A COURSE ON GROUP THEORY" by John S. Rose. You can find it here. Unfortunately, it is not well written, however it contains plenty of results. Moreover, it is not introductory and it focuses on the notion of group actions on sets and on groups, see Burnside Theorem and else. (I don' t know if you can find it free in online form)