15.2.1 - Definition of Subgroups
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Practice Questions
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What is a subgroup?
💡 Hint: Think about the definition of a group you learned before.
List the three main properties a subset must satisfy to be a subgroup.
💡 Hint: Recall our classroom discussion on subgroup conditions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What property must a subset satisfy to be a subgroup?
💡 Hint: Think of the subgroup conditions we discussed.
True or False: A subgroup can be empty.
💡 Hint: Remember the definition of a group.
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Challenge Problems
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Given a group G of order 15, list the possible orders of its subgroups. Prove your reasoning using Lagrange’s theorem.
💡 Hint: Find factors of 15.
Construct a subgroup for the group of permutations on three objects. Show all properties hold.
💡 Hint: Consider how permutations combine and find pieces that remain closed.
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