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SSC Pure Mathematics QUESTION #11203
Question 1
Let $G = \langle b: b^{17} = e\rangle$. Then $G$ can be generated by:
  • Any element of $G$
  • Any non-identity element of $G$✔️
  • $b$ and $b^{-1}$ are the only generators
  • Identity
Correct Answer Explanation
Since $|G| = 17$ is prime, every non-identity element has order 17 and hence generates $G$. By Lagrange's theorem, in a group of prime order every non-identity element is a generator. So $G$ can be generated by any non-identity element of $G$.