# Math Help - group terminology

1. ## group terminology

what is the group Z6 and the group Z3 x Z2. the numbers are subscripts btw

2. Originally Posted by poirot
what is the group Z6 and the group Z3 x Z2. the numbers are subscripts btw

Both are one and the same: the cyclic group of order 6 .

Tonio

3. Originally Posted by tonio
Both are one and the same: the cyclic group of order 6 .

Tonio
are they integers under addition, for example or is it just any cyclic group order 6? Thats what i'm after.

4. Originally Posted by poirot
are they integers under addition, for example or is it just any cyclic group order 6? Thats what i'm after.

$\mathbb{Z}_n$ is a group under addition modulo n, and $\mathbb{Z}_2\times \mathb{Z}_3$ is a group under

coordinatewise addition. Anyway, they both are isomorphic to a (or the, if you will) cyclic group of order 6.

Tonio