- #1
Mr Davis 97
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Homework Statement
Prove that a group has exactly one idempotent element.
Homework Equations
The Attempt at a Solution
So we need to show that the identity element is the unique idempotent element in a group.
First, we know that by definition of a group there is at least one element, e, such that ##e * e = e##.
Second, we need to show that there is at most one idempotent element. We do this by showing that if ##x*x=x## and ##y*y=y## then ##x=y##... This is as far as I get. Am I on the right track?