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3 cards from this section. Quick, good the night before a test.
What is a subgroup?
Think about the definition of a group you learned before.
List the three main properties a subset must satisfy to be a subgroup.
Recall our classroom discussion on subgroup conditions.
What property must a subset satisfy to be a subgroup?
Think of the subgroup conditions we discussed.
True or False: A subgroup can be empty.
Remember the definition of a group.
Given a group G of order 15, list the possible orders of its subgroups. Prove your reasoning using Lagrange’s theorem.
Find factors of 15.
Construct a subgroup for the group of permutations on three objects. Show all properties hold.
Consider how permutations combine and find pieces that remain closed.
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