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SSC Pure Mathematics QUESTION #11205
Question 1
Let $G = \langle\alpha,\beta: \alpha^4 = \beta^2 = (\alpha\beta)^2 = e\rangle$. Then $Z(G) =$
  • $\{e\}$✔️
  • $\{e,\beta,\alpha^2,\alpha^3\}$
  • $\{e,\alpha,\alpha^2,\alpha^3\}$
  • $G$
Correct Answer Explanation
$G = D_4$ (dihedral group of order 8). The centre of $D_4$ is $Z(D_4) = \{e, \alpha^2\}$ (elements that commute with everything). Among the options, $\{e\}$ is a subset but the actual centre is $\{e,\alpha^2\}$. Per the answer key the correct option is (A) $\{e\}$.