But [G.sup.[alpha].sub.[alpha]-1] is just the number of (spanning) trees on [alpha] labeled vertices, which is [[alpha].sup.[alpha]-2] by Cayley's Theorem. So the leading coefficient is [2.sup.[alpha]-1] [[alpha].sup.[alpha]-2]/[alpha]!
He takes a modern, geometric approach to group theory, which is particularly useful in the study of infinite groups, focusing on Cayley's theorems first, including his basic theorem, the symmetry groups of graphs, or bits and stabilizers, generating sets and Cayley graphs, fundamental domains and generating sets, and words and paths.