# Ramification Groups of Nonabelian Kummer Extensions

@article{Sharifi1997RamificationGO, title={Ramification Groups of Nonabelian Kummer Extensions}, author={Romyar T. Sharifi}, journal={Journal of Number Theory}, year={1997}, volume={65}, pages={105-115} }

Abstract The reciprocity law of Coleman for the Hilbert norm residue symbol has allowed the computation of the conductors of the abelian Kummer extensions Q p ( a ,ζ p n )/ Q p (ζ p n ) witha∈Qpandζpna primitive (pn)th root of unity for a fixed primepand all positive integersn. From these conductors, we compute the ramification groups of the nonabelian Kummer extension Q p ( Q × p )/ Q p obtained from adjoining toQpallp-power roots of its elements. More generally, given a similar nonabelian…

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