# Intersection of a Subgroup and the Normal Subgroup of a Group

Please address the following question: If H is a subgroup of G and N is a normal subgroup of G, show that H intersection N is a normal subgroup of H.

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Modern Algebra

Group Theory (XXXIX)

Subgroups of a Group

Normal Subgroups of a Group

If is a subgroup of and is ...

#### Solution Summary

In this response it is shown that if H is a subgroup of G and N is a normal subgroup of G, that H intersection N is a normal subgroup of H. The solution is detailed and well presented in an attached Word document.