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15.2.3. Corollary on Finite Groups
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3 cards from this lesson. Good the night before a test.
Try these first
- 1.
What is a subgroup?
Hint
Think about what group properties must hold.
- 2.
Define the closure property.
Hint
Consider how operations behave in a group.
- 3.
What is a subgroup?
- A subset that meets certain criteria
- Any subset of a group
- A group with fewer elements
Hint
Consider the definition of groups.
- 4.
True or False: Every subgroup has the same number of elements as its parent group.
Hint
Think about examples with smaller subsets.
- 5.
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.
- 6.
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.
Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
4 more questions available
Enrol freeQuiz
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
2 more questions available
Enrol freeChallenge Problems
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting