For any positive integer n greater than 1, the set of numbers between 1 and n which are relatively prime to n form a group with operation of multiplication modulo n. This applet provides a sort of picture of those groups. Each wedge in the circle represents an element of U(n). Generators are colored red, while other elements are shades of gray based upon their orders (darker gray for higher order). Not all of the U(n) are cyclic, so some do not have a generator. Moving the mouse up and down on the applet changes n, between 2 and 49.

 

Source code: unitaryGroups

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