computing character degrees via a galois connection

In a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$. however, the analysis when $|f|$ is a mersenne prime is more complicated, so certain cases were omitted from that paper.the present exposition, which is a reworking of the previous article, provides a uniform analysis over all the families, including the previously undetermined ones. in the group $crtimes{rm gal}(e/f)$, we use the galois connection to calculate stabilizers of linear characters, and these stabilizers determine the full character degree set. this is shown for each subgroup $cleq e^times$ which satisfies the condition that every prime dividing $|e^times :c|$ divides $|f^times|$.