1. ## Cyclic groups?

(a) Define what it means for s group to be cyclic.

(b) Give an example of an infinite cyclic group

(c) Determine whether the group U[15] = {1,2,4,7,8,11,13,14}, where multiplication is mod 15, is cyclic.

2. Originally Posted by Jason Bourne
(a) Define what it means for s group to be cyclic.
That is something you need to know from your textbook.

(b) Give an example of an infinite cyclic group
$\displaystyle \mathbb{Z}$
(c) Determine whether the group U[15] = {1,2,4,7,8,11,13,14}, where multiplication is mod 15, is cyclic.
Can you find a generator?

3. No, I cannot find any generators, so the group is not cyclic.

4. Originally Posted by Jason Bourne
No, I cannot find any generators, so the group is not cyclic.
That is correct. In general if $\displaystyle n>1$ then the group $\displaystyle \mathbb{Z}_n^{\text{x}}$ is cyclic if and only if $\displaystyle n=2,4,p^k,2p^k$ where $\displaystyle p$ is an odd prime.