Question

Does a field of order 64 has a subfield of order 32.

Answer 1

Hey Folk here is your answer.........
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Yaa A field of order 64 has a subfield of order 32 , because sub field takes the half of the order, so if the field order is 64 then the sub field order will be 32.

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Answer 2

Answer: No

Explanation     Given order of the field is 64 which means 2^6 find the divisor of prime power here prime is 2 and its power is 6. we just find the positive divisors of 6 that is (1,2,3,6) so possible subfields are (2^1,2^2,2^3,2^6). so that subfield of order 32 is not possible.