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Part CCSIR NET December 2023order-of-gl2-over-z-9

Order of gl2 over z 9

Let G be the group (under matrix multiplication) of 2 × 2 invertible matrices with entries from Z/9Z\mathbb{Z}/9\mathbb{Z}. Let a be the order of G. Which of the following statements are true?

  1. A.a is divisible by 343^{4}.✓ Correct
  2. B.a is divisible by 242^{4}.✓ Correct
  3. C.a is not divisible by 48.
  4. D.a is divisible by 363^{6}.

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Every group of order p² is cyclic

More on this topic

The chapter behind this: Group actions, the class equation and p-groups — free to read

From Groups › Group actions, class equation, p-groups

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