Algebra Book on how to write proper proofs in Group Theory

[jstrunk]

I am trying to learn group theory on my own from Schaum's Outline of Group Theory.
I chose this book because there are a lot of exercises with solutions, but I have several problems with it.
1) In many cases the author just makes some handwavey statement and I have to spend hours or days trying to figure out the what's behind his
pronouncement.
2) The solutions use too much English, as opposed to Math. English is imprecise and ambiguous. Maybe that's really how you do proofs in Group
Theory. This is the only book I have used, so i don't know. But it seems like clearer proofs could be made.
3) I often solve a problem in a different way that seems simpler to me, and I can't tell if I am missing some subtlety or if the author is being
unnecessarily convoluted. For instance, in many cases I think I can directly prove that G=H, say, but the author proves that G<or=H and H<or=G
so G=H.
The net result is that I never get to see what I consider to be a clear, full, proper proof of anything.
If I was taking a class, the teacher would be able to clear these things up, but on my own they are hard to deal with.
So I would appreciate any recommendations and a book that show how to write proper group theory proofs.

 

[fresh_42]

Well you can present your proofs here for cross checks, or on problems which you get stuck.
Here's a book for free: https://www.jmilne.org/math/CourseNotes/GT.pdf
but I would rather finish Schaum than to start something new.