Let $F$ be a field and $L$ a finite extension of $F$. Show that if $[L:F] = n$, then $L$ has at most $n$ distinct $F$-automorphisms.
Math Stack Exchange (MSE) has a dedicated tag [dummit-foote] . Virtually every exercise from the textbook has been asked, answered, and critiqued on MSE. solutions to abstract algebra dummit and foote
Several unofficial solution guides and "papers" are available online for Abstract Algebra (3rd Edition) Let $F$ be a field and $L$ a finite extension of $F$