The number of modular extensions of odd degree of a local field. (English) Zbl 1225.11154

Summary: The number of Galois extensions, up to isomorphism, of a local field whose Galois groups are isomorphic to the modular group \(M_{p^{m}}=\langle x,y \mid x^{p^{m-1}}=y^{p}=1,y^{-1}xy=x^{p^{m-2}+1}\rangle\), where \(p\) is an odd prime, is counted.


11S20 Galois theory
Full Text: DOI Euclid


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