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isaiah
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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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