Math Problem Statement

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Solution

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Math Problem Analysis

Mathematical Concepts

Group Theory
Subgroups
Normal Subgroups

Formulas

Definition of a normal subgroup: N ⊲ G
Product of subgroups: NH = {nh | n ∈ N, h ∈ H}
Subgroup criteria: closure, identity, and inverses

Theorems

Theorem: The product of a normal subgroup and another subgroup is a subgroup.
Normal subgroup property: NH = HN

Suitable Grade Level

Undergraduate level in abstract algebra

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