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Part CCSIR NET December 2024no-finite-group-is-divisible

No finite group is divisible

A group G is said to be divisible if for every y ∈ G and for every positive integer n, there exists x ∈ G such that . Which of the following groups are divisible?

  1. A. with ordinary addition✓
  2. B. \ {0} with ordinary multiplication✓
  3. C.The cyclic group of order 5
  4. D.The symmetric group

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.

See pricing

50 are analysed free — try those first.

Related counterexample: (ℤ/2^kℤ) is cyclic for every k

More on this topic

The chapter behind this: Structure of finite abelian groups — free to read

From Groups › Finite abelian groups

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