Homework 23

Read: Finish reading Chapter 6.

• Example 6.73 is really important for the problems that follow, so please read it carefully.

Turn in: 6.71, 6.74, 6.76, 6.79, 6.80

• For 6.71 you mainly just need to use the definition of $\operatorname{Aut}(K/F)$ which is $\operatorname{Aut}(K/F) = \{\alpha \in \operatorname{Aut}(K) \mid \forall f\in F, \alpha(f) = f\}$.
• When doing 6.80(4), read over 6.72 about why the subgroup lattice is upsidedown.

Please try (but do not turn in): 6.70, 6.72, 6.77