A **multiplicative group** is a mathematical structure consisting of a set equipped with a binary operation that satisfies certain properties. Specifically, a multiplicative group is a set \( G \) along with a binary operation (commonly denoted as multiplication) that has the following characteristics: 1. **Closure**: For any two elements \( a, b \in G \), the result of the operation \( a \cdot b \) is also in \( G \).
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