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May 8, 2014 at 22:38 comment added Henri Johnston Yes (assuming $l \neq p$, of course).
May 8, 2014 at 18:41 comment added Torsten Schoeneberg Just for clarity (I just confused myself for a minute): What you are saying in your third paragraph is that either $K$ contains all $p$-th roots of unity (so we are in the Kummer case), or there are no ramified Galois extensions of degree $p$ at all (so the unramified is the only one).
Jul 4, 2011 at 9:12 vote accept Stefan Keil
Jun 23, 2011 at 17:08 history answered Henri Johnston CC BY-SA 3.0