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I am trying to figure out the effect of a field automorphism on a field with a non prime subfield.

Say for example [tex]F_{2^{29}}[/tex], [tex]F_{2^{58}}[/tex] and [tex]F_{2^{116}}[/tex]

Let [tex]\alpha \in F_{2^{58}}[/tex]\[tex]F_{2^{29}} [/tex]

Under [tex]{\sigma}^{i}, 1 \le i \le 58[/tex] do we get any case where [tex]\alpha[/tex] becomes an element of [tex]F_{2^{29}}[/tex] ?

If not why not since the orbit of [tex]\alpha[/tex] under this automorphism will be 58.

Does it mean that the other elements shift to [tex]F_{2^{116}}[/tex]?

Thanks in advance.

Isaiah.

Say for example [tex]F_{2^{29}}[/tex], [tex]F_{2^{58}}[/tex] and [tex]F_{2^{116}}[/tex]

Let [tex]\alpha \in F_{2^{58}}[/tex]\[tex]F_{2^{29}} [/tex]

Under [tex]{\sigma}^{i}, 1 \le i \le 58[/tex] do we get any case where [tex]\alpha[/tex] becomes an element of [tex]F_{2^{29}}[/tex] ?

If not why not since the orbit of [tex]\alpha[/tex] under this automorphism will be 58.

Does it mean that the other elements shift to [tex]F_{2^{116}}[/tex]?

Thanks in advance.

Isaiah.

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