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Part CCSIR NET June 2024order-is-an-lcm-not-a-cycle-length

Order is an lcm not a cycle length

Which of the following numbers are order of some element of the symmetric group S5S_{5}?

  1. A.3✓ Correct
  2. B.4✓ Correct
  3. C.5✓ Correct
  4. D.6✓ Correct

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, and why this one tests standard counterexample.

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50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Related counterexample: Aₙ is simple for every n ≥ 3

More on this topic

The chapter behind this: Permutation groups — cycle type, sign and conjugacy — free to read

From Groups › Permutation groups: cycles, sign, conjugacy in S_n and A_n

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