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 $C \rtimes {Gal} (E/F)$. 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 $C\rtimes{\rm Gal(E/F)}$, 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 $C\leq E^\times$ which satisfies the condition that every prime dividing $|E^\times :C|$ divides $|F^\times|$.
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Lewis, M., & McVey, J. (2015). Computing character degrees via a Galois connection. International Journal of Group Theory, 4(1), 1-6. doi: 10.22108/ijgt.2015.6212
MLA
Mark L. Lewis; John K. McVey. "Computing character degrees via a Galois connection". International Journal of Group Theory, 4, 1, 2015, 1-6. doi: 10.22108/ijgt.2015.6212
HARVARD
Lewis, M., McVey, J. (2015). 'Computing character degrees via a Galois connection', International Journal of Group Theory, 4(1), pp. 1-6. doi: 10.22108/ijgt.2015.6212
VANCOUVER
Lewis, M., McVey, J. Computing character degrees via a Galois connection. International Journal of Group Theory, 2015; 4(1): 1-6. doi: 10.22108/ijgt.2015.6212
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