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2 cards from this section. Quick, good the night before a test.
Define the identity element.
Think about what happens when something added to 0 or multiplied by 1.
What does it mean for an element to be a generator?
What structure would you use to generate other elements?
What is the identity element in group theory?
Think about what happens when combined with other elements.
True or False: Every group can have more than one identity element.
Consider the definition of identity.
In a cyclic group of order 12, what is the order of the generator? Prove your reasoning.
Consider how many unique group elements can be formed by repeated application of the generator.
For group G with elements g, g², g³ where g is a generator, determine if g⁴ can be expressed in terms of the existing elements.
Check if g raised to a high exponent remains in the scope of the original elements.
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