# Normalizer of a Subgroup of a Group

Modern Algebra

Group Theory (XLV)

Normalizer of a Subgroup of a Group

Centralizer of a Subgroup of a Group

Normalizer 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 N(H) is a subgroup of G.

The fully formatted problem is in the attached file.

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#### Solution Summary

This solution is comprised of a detailed explanation to prove that N(H) is a subgroup of a group G,

where H is a subgroup of G and N(H) = {g belongs to G|gHg^-1 = H}. The solution is detailed and well presented.