Suppose a and b are in a group, a has odd order, and . .

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- Sep 8th 2007, 11:04 AMtttcomraderElement with odd order
Suppose a and b are in a group, a has odd order, and . .

- Sep 9th 2007, 11:20 PMOpalg
In the relation , take the inverse of both sides, to get . It follows that . By the same calculation, , and so on. In fact, is equal to if

*k*is odd, and if*k*is even.

Now take*k*to be the order of*a*, which is odd. Then (the identity element of the group), and . But since*k*is odd, this is also equal to . So and therefore .