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Galois Theory — Thomas Judson
Mathematics — Abstract Algebra · finite-fields-degree-extensions
Problem Calculate each of the following.
(a) [ G F ( 3 6 ) : G F ( 3 3 ) ] [\mathrm{GF}(3^6) : \mathrm{GF}(3^3)] [ GF ( 3 6 ) : GF ( 3 3 )] [ G F ( 128 ) : G F ( 16 ) ] [\mathrm{GF}(128) : \mathrm{GF}(16)] [ GF ( 128 ) : GF ( 16 )] [ G F ( 625 ) : G F ( 25 ) ] [\mathrm{GF}(625) : \mathrm{GF}(25)] [ GF ( 625 ) : GF ( 25 )] [ G F ( p 12 ) : G F ( p 2 ) ] [\mathrm{GF}(p^{12}) : \mathrm{GF}(p^2)] [ GF ( p 12 ) : GF ( p 2 )] Browse the problem library