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Unformatted text preview: we see that bd = 1. It is then not dicult to discuss all possibilities. p426, E21 Since x 2 = 1 has at most 2 solutions, 2 is the only element of order 2. That means, any element which is not 0 , 1 , 2 is of order either 13 or 26. If has order 13, then 13 = 1, then (2 ) 13 = 2 13 13 = 2 6 = 1, so 2 does not have order 13. Therefore it must have order 26. Suppose that has order 26, then 13 6 = 1. In addition, ( 13 ) 2 = 1, so 13 = 2. Then (2 ) 13 = 2 13 13 = 2 14 = 1. So 2 has order 13. Note that the converse direct is direct from the previous argument, using the fact that 2 2 = . 1...
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This note was uploaded on 09/05/2011 for the course MATH 3360 taught by Professor Billera during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 BILLERA
 Math, Algebra

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