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

- Apr 2nd 2010, 10:58 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.

- Apr 3rd 2010, 01:30 AMFancyMouse
Do a long division on the exponent.

- Apr 3rd 2010, 02:42 PMrainyice
- Apr 3rd 2010, 06:00 PMFancyMouse
- Apr 3rd 2010, 06:12 PMrainyice
- Apr 3rd 2010, 07:10 PMchiph588@
, where .

So,

Since , what is the only such that gives ?