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Part CCSIR NET June 2024subfields-count-divisors-of-the-exponent

Subfields count divisors of the exponent

For which of the following values of q, does a finite field of order q have exactly 6 subfields?

  1. A.✓
  2. B.✓
  3. C.✓
  4. D.✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Related counterexample: An algebraic extension is a finite extension

More on this topic

The chapter behind this: Field extensions, degrees and splitting fields — free to read

From Rings and Fields › Field extensions, splitting fields, finite fields

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