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Mar10-12, 12:40 AM
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Quote Quote by PennState666 View Post
yes of course I just wanted to be refreshed and reassured...
Z2 x Z3 = {([0],[0]), ([0],[1]), ([0],[2]), ([1],[0]), ([1],[1]), ([1],[2])}...
I cannot grasp how this could be generated by a single element though?
Look at the six elements. In order for the group to be generated by one element, clearly that element can't have a [0] in either of the two positions of the ordered pair. So that only leaves two candidates: either ([1],[1]) or ([1],[2]). Why not try each and see if it works? Just add it to itself over and over and see if you can generate the group.