Thread: 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.

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

(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?

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

Originally Posted by Jason Bourne

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

That is correct. In general if then the group is cyclic if and only if where is an odd prime.