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4 cards from this section. Quick, good the night before a test.
Define what a cyclic group is.
Think about how one element can create others.
What is the identity element in a group?
Consider what element would keep others 'the same.'
What is a cyclic group?
Think about what defines the word 'cyclic'.
True or False: In any group, the identity and inverse elements are unique.
Recall the properties of group definitions.
Given a cyclic group of order 8 generated by g, list the elements of the group.
Start with the generator and calculate its powers.
If a generator of a cyclic group has order 12, what can be said about the powers of this generator?
Consult your knowledge on the structure of cyclic groups.
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