15.2.3 - Corollary on Finite Groups
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Practice Questions
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What is a subgroup?
💡 Hint: Think about what group properties must hold.
Define the closure property.
💡 Hint: Consider how operations behave in a group.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a subgroup?
💡 Hint: Consider the definition of groups.
True or False: Every subgroup has the same number of elements as its parent group.
💡 Hint: Think about examples with smaller subsets.
2 more questions available
Challenge Problems
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Given the set of real numbers, prove or disprove that the set of negative rational numbers is a subgroup under addition.
💡 Hint: Check closure when adding two elements from the subset.
Consider a group of order 12 and a subgroup of order 3. How many distinct cosets can be formed from this subgroup?
💡 Hint: Utilize the relationship from Lagrange’s theorem.
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