(New page: How do you prove that an element and its inverse have the same order? I understand the idea but do not know how to prove it. -Wooi-Chen) |
|||
| Line 2: | Line 2: | ||
-Wooi-Chen | -Wooi-Chen | ||
| + | |||
| + | |||
| + | ---- | ||
| + | I thought this worked as a proof. | ||
| + | |||
| + | <math>g^k=1</math> element g having order of k | ||
| + | <math>(g^k)^-1=(1)^-1</math> | ||
| + | <math>g^-k=1</math> | ||
| + | <math>(g^-1)^k=1</math> inverse of g having order of k | ||
| + | |||
| + | This could be wrong, but it makes sense. | ||
| + | |||
| + | -Daniel | ||
Revision as of 17:23, 16 September 2008
How do you prove that an element and its inverse have the same order? I understand the idea but do not know how to prove it.
-Wooi-Chen
I thought this worked as a proof.
$ g^k=1 $ element g having order of k $ (g^k)^-1=(1)^-1 $ $ g^-k=1 $ $ (g^-1)^k=1 $ inverse of g having order of k
This could be wrong, but it makes sense.
-Daniel
