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3 cards from this section. Quick, good the night before a test.
What is the identity element in a group?
It is represented by the letter e in many mathematical contexts.
Define an inverse element.
Think about reversing an operation.
What does the identity element do in a group?
Consider the definition of identity.
Can a group have multiple identity elements?
Think about the properties of identity.
Show that in any finite group, a generator's order must equal the group's order.
Think about all elements and how repetition constrains output.
In a cyclic group of odd order, show every element must also have an odd order.
Consider how inverses match within powers.
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