Practice Cosets (15.2.5) - Subgroups - Discrete Mathematics

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6 sample questions

Question 1.
Define a left coset in your own words.
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Consider which side the group element appears.
Question 2.
What is the significance of Lagrange's theorem?
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Think about relationships between subgroups and their parent groups.
3Question 3.
What is a left coset?
- A set of elements formed by subtracting a subgroup from a group
- A collection formed by multiplying a group element with a subgroup
- The same as a right coset
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Think about the multiplication order.
4Question 4.
True or False: The order of a subgroup divides the order of the group.
- True
- False
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Consider the implications of subgroup sizes.
Question 5.
Given a group of integers under addition modulo 8, identify the subgroup generated by 2. List the left cosets of this subgroup.
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Calculate by adding the group element to each member of the subgroup.
Question 6.
In a group of order 12, if a subgroup has order 3, determine the number of distinct left cosets.
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Use Lagrange's theorem to divide the total group order by the order of the subgroup.

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