Lagrange's Theorem states that in a finite group, the order (number of elements) of any subgroup divides the order of the entire group.

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Here are five related questions:
1. How is Lagrange's theorem used in group theory?
2. Can you give an example of Lagrange’s theorem with a specific group?
3. What are the implications of Lagrange’s theorem for cyclic groups?
4. How does Lagrange’s theorem connect with cosets?
5. What is the significance of Lagrange’s theorem in Galois theory?

**Tip:** The theorem is only valid for finite groups; it doesn't necessarily apply to infinite groups.

Lagrange's Theorem states that in a finite group, the order of any subgroup divides the order of the entire group. This fundamental theorem in group theory is crucial for understanding subgroup structures and cosets. Explore its applications in various fields, including Galois theory.

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