Thread: group terminology

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

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.

is a group under addition modulo n, and is a group under

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

Tonio