Where can I find a high-level overview of Adyan’s original proof of the existence of finitely generated infinite groups with finite exponent?
If possible, would an expert please write a short synopsis of this proof here on MO?
Many years ago at Illinois, Ken Appel took notes for lectures on combinatorial group theory given by Adyan. He told me once that Adyan had said that the key thing missing from Britton’s approach to the general Burnside problem was the notion of a cascade. I’d like to know, for example, why this is the case. How, precisely, is Adyan's proof related to Britton's attempt? Is the former a perturbation of the latter in which cascades resolve the inconsistency? If so, can one succinctly say how?
In an English translation of S. I. Adian, “An axiomatic method of constructing groups with given properties”, Uspekhi Mat. Nauk, 32:1(193) (1977), 3–15, we find, regarding the interlocking facts to be proved by simultaneous induction on the rank:
"...as the reader accumulates experience and gradually forms intuitive pictures of the relevant concepts, our proofs become less formal..."
What are these intuitive pictures? (Of course, I don't expect an answer for this.)
Is Adyan's notion of cascade used anywhere else in group theory today? (Or has this idea been totally abandoned for Olshanskii's diagrammatic method.)
I apologize for not including a definition of cascade, but the ability to do so concisely is implicitly part of the question!