# cyclic group of order m

• November 19th 2009, 05:57 AM
apple2009
cyclic group of order m
If G=<a> is a cyclic group of order m generated by an element a∈G, then for each divisor r of m exhibit explicitly an element c∈G of order r.
• November 19th 2009, 07:36 AM
Drexel28
Have you even tried this? This really isn't too hard. It doesn't even ask you to show that the element you find with order $r$ is unique. If $r|m$ what can we say about $a^{\frac{m}{r}}$?