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4 cards from this section. Quick, good the night before a test.
What are the four axioms that define a group?
Use the acronym C-A-I-I.
Give an example of a group under addition.
Think about the properties of integers.
Which property ensures that the result of an operation on two elements is still in the set?
Think about how operations interact with set membership.
True or False: Every group operation must be commutative.
Recall the definition of an Abelian group.
Prove that any finite subset of a group is also a group under the same binary operation, citing each of the group axioms.
Focus on the properties of the larger group.
Given the set of integers modulo n, discuss how it forms a group with addition, relating it to all four axioms.
Revisit properties of modulo arithmetic.
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