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Oct 22, 2010 at 12:57 comment added Gerry Myerson Oh. OK. Say, is someone going through this discussion downvoting answers? I see three answers at minus 1.
Oct 22, 2010 at 10:52 comment added KConrad I had changed the "Let... then" to "If... then" because it was used in a single sentence, which is not the same way it is used in the quote from Adamson's book (where it's "Let.... Then").
Oct 22, 2010 at 10:37 comment added Gerry Myerson The distinction OP makes between "setting the scene" and the "real" hypotheses is, I confess, not clear to me. For what it's worth, I was more-or-less quoting from Adamson, Introduction To Field Theory: "Let $K$ be a separable normal extension of finite degree $n$ over a subfield $F$, with Galois group $G$. Then $G$ has order $n$." I even took the "Let ... then" construction from Adamson.
Oct 22, 2010 at 10:21 comment added KConrad Gerry, one usually sets the stage for this by starting with a finite extension K/F. Then if (and only if) K is normal and separable over F, #Aut(K/F) = [K:F]. That's just my two (not three) cents...
Oct 22, 2010 at 10:18 history edited KConrad CC BY-SA 2.5
changed "let...,then" to "if...,then"
Oct 22, 2010 at 10:02 history answered Gerry Myerson CC BY-SA 2.5