I'm trying to find an example to show the map $\sigma_p : F \rightarrow F$ given by $\sigma_p(a)=a^p$ for $a\in F$ need not be an automorphism in the case that F is infinite. I'm lost as to where to start. Any pointers?
Frobenius Auto need not be an automorphism if F is infinite
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abstract-algebra
field-theory