I am searching for a book on group theory that follows in the style of textbooks written for math students (since I was one), but that covers all (or at least most) topics that would be needed in physics, such as in QFT for example (Think of the topics in Zee's Group theory in a nutshell).

My problem with Zee is that it is too verbose and not as mathematically rigorous as I'd prefer (I can understand the concepts better when they are presented in a formal mathematical way). And my problem with other standard group theory books for math is that they usually do not cover all the topics needed for physics (Lie Algebras, Poincare groups...)

A single or many-book-combination recommendation that would fill in these criteria is welcome.