Math Help - Factor group order question

1. Factor group order question

$ \cong C_9 \cong $ and $G = \times $.
What is the factor group $G/$ order and write it as the direct product of cyclic groups.

Isn't $G/$ has order 3(correct me if I'm wrong) and I need some help on this the second part "write it as the direct product of cyclic groups".

Thank you for your help.

2. Originally Posted by kleenex
$ \cong C_9 \cong $ and $G = \times $.
What is the factor group $G/$ order and write it as the direct product of cyclic groups.

Isn't $G/$ has order 3(correct me if I'm wrong) and I need some help on this the second part "write it as the direct product of cyclic groups".

Thank you for your help.
Instead of $\left< x^3,y^3\right>$ I think you mean $\left \times \left< y^3 \right>$. Then it means, $G/\left \times \left< y^3 \right> = \left< x \right> \times \left< y\right> / \left \times \left< y^3 \right> \simeq \left< x \right> / \left \times \left< y\right> / \left< y^3 \right>\simeq \mathbb{Z}_6\times \mathbb{Z}_6$.