# Thread: Prove that the finite cyclic group is isomorphic

1. ## Prove that the finite cyclic group is isomorphic

Please can you help me with the following question:

Prove that every finite cyclic group is isomorphic to Z/(n) for nEZ

(where Z is an integer)

I really don't know where to start on this question but I know that if the group is bijective then it is isomorphic. Do I need to use this as a starting point?

Any help would be really greatful

2. Originally Posted by mathspeep
Please can you help me with the following question:

Prove that every finite cyclic group is isomorphic to Z/(n) for nEZ

(where Z is an integer)

I really don't know where to start on this question but I know that if the group is bijective then it is isomorphic. Do I need to use this as a starting point?

Any help would be really greatful
hi mathspeep!
welcome to the forum.
there are problems with your notations. you must first get those right. moreover you write "nEZ (where Z is an integer)". this does not make much sense. read the original problem. understand what is being asked... take your time and when you start to see that the problem really makes sense then re-attempt it. if then you can't do it then re-post it along with your attempt. Me and others will be happy to help.

3. if G is cyclic, it has a single generator. let's call it x.

can you think of a mapping that takes x^k to an element of Z/nZ that might be a homomorphism?

(use the properties of exponents. if G is isomorphic to Z/nZ, what should the order of x be?).