15.2.5 - Cosets
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Practice Questions
Test your understanding with targeted questions
Define a left coset in your own words.
💡 Hint: Consider which side the group element appears.
What is the significance of Lagrange's theorem?
💡 Hint: Think about relationships between subgroups and their parent groups.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a left coset?
💡 Hint: Think about the multiplication order.
True or False: The order of a subgroup divides the order of the group.
💡 Hint: Consider the implications of subgroup sizes.
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Challenge Problems
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Given a group of integers under addition modulo 8, identify the subgroup generated by 2. List the left cosets of this subgroup.
💡 Hint: Calculate by adding the group element to each member of the subgroup.
In a group of order 12, if a subgroup has order 3, determine the number of distinct left cosets.
💡 Hint: Use Lagrange's theorem to divide the total group order by the order of the subgroup.
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