Practice Corollary On Finite Groups (15.2.3) - Subgroups - Discrete Mathematics

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6 sample questions

Question 1.
What is a subgroup?
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Think about what group properties must hold.
Question 2.
Define the closure property.
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Consider how operations behave in a group.
3Question 3.
What is a subgroup?
- A subset that meets certain criteria
- Any subset of a group
- A group with fewer elements
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Consider the definition of groups.
4Question 4.
True or False: Every subgroup has the same number of elements as its parent group.
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Think about examples with smaller subsets.
Question 5.
Given the set of real numbers, prove or disprove that the set of negative rational numbers is a subgroup under addition.
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Check closure when adding two elements from the subset.
Question 6.
Consider a group of order 12 and a subgroup of order 3. How many distinct cosets can be formed from this subgroup?
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Utilize the relationship from Lagrange’s theorem.

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