Abstract
Kaplansky's hypothesis A concerning valued fields is put into a Galois theoretic setting. Accordingly, Kaplansky's theorem on maximal immediate extensions can be deduced from the Schur-Zassenhaus theorem about conjugacy of complements in profinite groups. Some generalization of Kaplansky's theory is given, concerning maximal purely wild extensions.
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Kuhlmann, F.V., Pank, M. & Roquette, P. Immediate and purely wild extensions of valued fields. Manuscripta Math 55, 39–67 (1986). https://doi.org/10.1007/BF01168612
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DOI: https://doi.org/10.1007/BF01168612