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H is normal in G if and only if N(H) = G.

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Modern Algebra
Group Theory (XLVIII)
Normal Subgroups of a Group
Normalizer of a Subgroup of a Group
Centralizer of a Subgroup of a Group

If H is a subgroup of G, let N(H) = {g belongs to G|gHg^-1 = H}. Prove that H is normal in G if and only if N(H) = G.

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Solution Summary

It is proven that H is normal in G if and only if N(H) = G. The solution is detailed and well presented.
Normalizers of subgroups are investigated. The solution is detailed and well presented.

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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