The Fixed Point Subspace of an Element

We begin with a detailed look at Hall–Higman theory, as well as Schult’s theorem. These results lead to better bounds on the dimensions of certain fixed-point subspaces than we proved in earlier chapters. We then use these improved bounds in the discussion of Dolfi’s powerful result, which shows if G is solvable and acts coprimely on K via automorphisms, then there are two elements of K whose centralizers in G intersect trivially. This proof draws on many of the results and techniques we have established so far.