mechnight Posted March 28, 2015 Report Share Posted March 28, 2015 (edited) 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... Edited March 28, 2015 by mechnight Reply Link to post Share on other sites More sharing options...
ctrls Posted March 28, 2015 Report Share Posted March 28, 2015 Yes, it is the element itself. More precisely, the order of an element is defined as the smallest positive integer such that , where is the identity element. Hence an element is order 1 if (so if it is the identity). Reply Link to post Share on other sites More sharing options...
mechnight Posted March 28, 2015 Author Report Share Posted March 28, 2015 Thanks! Reply Link to post Share on other sites More sharing options...
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