If a is an element of order m in a group G and a^(k) = e, prove that m divides k.

- April 2nd 2010, 09:58 PMrainyiceIf a is an element of order m in a group G and a^(k) = e, prove that m divides k.
If a is an element of order m in a group G and a^(k) = e, prove that m divides k.

- April 3rd 2010, 12:30 AMFancyMouse
Do a long division on the exponent.

- April 3rd 2010, 01:42 PMrainyice
- April 3rd 2010, 05:00 PMFancyMouse
- April 3rd 2010, 05:12 PMrainyice
- April 3rd 2010, 06:10 PMchiph588@
, where .

So,

Since , what is the only such that gives ?