What does K^Aut(K/F) mean?

>>8185682
Aut is for autistic
K/F is for Kentucky Fried

>>8185719
What is this? /pol/..?
That's Aut for gold/time, K for Potassium and F for Fluorine. Galois was a master alchemist back in the day.

>>8185682
Aut(K) is the autism group of the field K.

>>8185682
usually S^G means the points of S fixed pointwise by G

>>8185750
this. I assume its the fixed field without even having looked at the picture

>>8185750
which is why K^Aut(K/F) means the fixed points of K under the action of Aut(K/F). you know at least F is a subset of K^Aut(K/F) by definition of Aut(K/F) (automorphisms of K that fix F) but this theorem tells you that in fact it is exactly F, i.e. for every automorphism in Aut(K/F) there's something in K but not in F that gets acted on non-trivially

>>8185682
I know for a fact whatever you are reading has defined this notation. For a field K and a subgroup G of Aut(K), we define [math]K^G := \{x \in K : g(x)=x \;\forall g \in G \}[/math].

>>8185750
thanks

>>8185763
>I know for a fact whatever you are reading has defined this notation.

It has not.
http://www.pitt.edu/~gmc/algebra/galoistheory.pdf

This notation first appears on page 11, in this proof.

>>8185774
I've never seen an introductory Galois theory reading not define that, but it looks like these are class notes and the reader is supposed to be familiar with the notation from class/the textbook. My mistake.

>>8185787
Yeah I just wanted to read something that could teach me the fundamentals as quick as possible.

>>8185996
I think Keith Conrad should have something on his webpage. That man writes the absolute best expository notes. He made tensor products sensible to me.