Practice Lagrange's Theorem (15.2.6) - Subgroups - Discrete Mathematics

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6 sample questions

Question 1.
Define a subgroup in your own words.
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Think about the properties a subset must hold to be a group.
Question 2.
What does Lagrange's Theorem state?
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Consider how the number of elements correlates.
3Question 3.
What does Lagrange's Theorem state?
- The sum of group elements
- The order of a subgroup divides the order of the group
- Subgroups are always finite
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Recall the relationship between group sizes.
4Question 4.
True or False: A subgroup can be empty.
- True
- False
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Link to the definition of subgroup.
Question 5.
Given the group S3 (symmetric group of order 6), identify the subgroups and demonstrate how Lagrange’s Theorem applies.
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Use the concepts of permutations to explore subgroup structures.
Question 6.
Construct a non-trivial group of order 12 and apply Lagrange’s Theorem to determine possible subgroup orders.
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List divisors of the group order and check group structure properties.

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