15.2.6 - Lagrange's Theorem
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Practice Questions
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Define a subgroup in your own words.
💡 Hint: Think about the properties a subset must hold to be a group.
What does Lagrange's Theorem state?
💡 Hint: Consider how the number of elements correlates.
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Interactive Quizzes
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What does Lagrange's Theorem state?
💡 Hint: Recall the relationship between group sizes.
True or False: A subgroup can be empty.
💡 Hint: Link to the definition of subgroup.
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Challenge Problems
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Given the group S3 (symmetric group of order 6), identify the subgroups and demonstrate how Lagrange’s Theorem applies.
💡 Hint: Use the concepts of permutations to explore subgroup structures.
Construct a non-trivial group of order 12 and apply Lagrange’s Theorem to determine possible subgroup orders.
💡 Hint: List divisors of the group order and check group structure properties.
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