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SSC Pure Mathematics QUESTION #1286
Question 1
A subgroup \(H\) of a group \(G\) is called normal if for all \(g\in G\):
  • gH=H
  • gHg^{-1}\subseteq H✔️
  • H contains the identity
  • H is abelian
Correct Answer Explanation
A subgroup \(H\) is normal in \(G\) if \(gHg^{-1}=H\) (equivalently \(gHg^{-1}\subseteq H\)) for all \(g\in G\). This means left and right cosets coincide: \(gH=Hg\) for all \(g\in G\). Normal subgroups are the kernels of homomorphisms.