That concludes the end of the series of notes on Group Theory.
Has it been successful? I don’t know, but I’m reasonably pleased with the way the notes turn out, except the fact that there’s a huge disparity between the level of the first chapter and the last. In Chapter I, a reasonably motivated pre-university student should be able to understand everything. On the other hand, Chapter XII is at the level of an advanced undergraduate (probably 3rd or 4th year).
In other words, the beginning reader should not expect to be able to comprehend everything from alpha to omega. That being said, I’d urge the reader to at least persist until Chapter VIII – the Sylow theorems, which are exceptionally alluring even to someone who’s not particularly inclined towards group theory.
The main point of the notes is not to write another textbook on group theory. [ With about a thousand such texts available, does the world really need another one? ] Rather, it’s to document things which I wish someone had told me, the little moments of epiphany where the light bulb went off and I wanted to yell to the textbook, “why the heck didn’t you say so?”. Another purpose is to collect the best bits & proofs from various books. For example, while Herstein’s Topics in Algebra is a great book all-in-all, its approach to Sylow theorems is horribly dull. Hence I’ve used the approach in Hungerford’s Algebra instead.
Please leave comments. Error corrections are always welcome and appreciated. Suggestions on what works best for a set of notes like this will also help – though there’s no guarantee they will be implemented.