# 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}
}
• R. Sharifi
• Published 1 July 1997
• Mathematics
• Journal of Number Theory
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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