what is the group Z6 and the group Z3 x Z2. the numbers are subscripts btw
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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
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.
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. $\displaystyle \mathbb{Z}_n$ is a group under addition modulo n, and $\displaystyle \mathbb{Z}_2\times \mathb{Z}_3$ is a group under coordinatewise addition. Anyway, they both are isomorphic to a (or the, if you will) cyclic group of order 6. Tonio
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