# Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?

1) Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$? Why or why not? ($\mathbb{Z}/\langle n\rangle$ is defined to be the factor group of $\mathbb{Z}$ determined by $\langle n\rangle$.)

I guess I'm having trouble understanding factor groups (quotient groups make much more sense) and cyclic groups. My textbook isn't the best at explaining what's going on. I just chose some past homework problems that looked related to my problems.

This is my first abstract algebra course and I'm floundering a lot.

• Try to prove this fact: The homomorphic image of a cyclic group is cyclic. – Amr Sep 15 '13 at 22:02