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SSC Pure Mathematics QUESTION #11207
Question 1
Inner automorphisms of $Q = \{\pm 1, \pm i, \pm j, \pm k\}$ is:
  • $\{e\}$
  • $C_2\times C_2$✔️
  • $Q$
  • $C_4$
Correct Answer Explanation
The group of inner automorphisms $\text{Inn}(Q) \cong Q/Z(Q)$. For the quaternion group $Q_8$, the centre is $Z(Q_8) = \{1,-1\}$, of order 2. So $\text{Inn}(Q_8) \cong Q_8/\{1,-1\} \cong C_2\times C_2$ (Klein four-group), which has order 4.