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3 cards from this section. Quick, good the night before a test.
What does closure mean in group theory?
Think about what happens when you add two integers.
Identify the identity element in the group of integers with addition.
What number serves as a neutral element in addition?
Which of the following is not a property of a group?
Focus on the fundamental group axioms.
True or False: The set of natural numbers (excluding zero) is a group under addition.
Consider addition's identity and inverses.
Demonstrate that the set of matrices of size 2x2 under addition forms a group.
Consider how matrices add together and whether their operations fit the group properties.
Prove that the group of integers modulo n under addition isn't an abelian group if n is odd.
Consider how addition behaves under modulo conditions with odd-equal sums.
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