External direct products of cyclic groups

[lostNfound]

I'm wondering if anyone can help me with learning how to write groups as an external direct product of cyclic groups.

The example I'm looking at is for the subset {1, -1, i, -i} of complex numbers which is a group under complex multiplication. How do I express it as an external direct product of cyclic groups?

 

[micromass]

The group you posted IS cyclic.

 

[lostNfound]

Right. I understand that the subset of complex numbers shown is a group under multiplication, and I know that it itself is cyclic with i and -i both being generators, but I know it isn't expressed as an external direct product of cyclic groups.

 

[micromass]

Right. I understand that the subset of complex numbers shown is a group under multiplication, and I know that it itself is cyclic with i and -i both being generators, but I know it isn't expressed as an external direct product of cyclic groups.

It's a product with one factor.