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Order of elements in a group?


mechnight

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Hey guys!

 

We've recently started studying the option, and I have some troubles understanding how to find the order of the element in a group. Soo here's the question:

 

The binary operator * is defined for a, b  being real numbers by a * b = a + b – ab. The domain of * is now reduced to S = {0, 2, 3, 4, 5, 6} and the arithmetic is carried out modulo 7. Determine the order of each element in S. 

 

Could anyone shed some light on this? Thanks! :)

 

Edit: I think I've got it, but just in case? Is the first order-element the element itself, or when the operation is applied only once? I'm going with the first (the element), but if anyone could clarify... :D

Edited by mechnight
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