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http://bookboon.com/en/textbooks/mathematics/an-introduction-to-group-theory I came across this book randomly and I'm sure someone may be interested in this. To be honest, I haven't read the first 3 chapters that relate to group theory, so I'm unsure if the concept is self-contained or if it assumes knowledge regarding abstract algebra already. I did a quick read through the last chapter, where the music theory is presented. If a person is interested in how group theory can be used to describe musical relations, then it's a fairly interesting and straight forward read. I think, if someone here has read or studied abstract algebra and had a hard time understanding typical "concrete" examples, but understands music, then this book can be useful. The topics presented in the book are rather basic when it comes to music, but it should be fairly obvious on how to extend the concepts to more complex problems. If anyone else is familiar with the subject at say the typical undergraduate level care to weigh in and give their opinion on the matter that would be appreciated. I may be interested in teaching a summer course on this, but I'm unsure if the book is suitable or the material really that interesting.

Is there any nontrivial application to music in that book? I dunno. Not gonna read the whole thing just to find out though

The first one by doing the second one ;). I was hoping to make you realize that you were over thinking it. Anything can work in certain contexts, all that matters where 'tonic prolongation' is concerned, is that you successfully create the feeling of it. As far as chords, my favorite are the borrowed minor iv, chords a 3rd away from other keys, and chords a tritone away. Late 19th century/Early 20th century Russian composers loved doing this kind of thing.