Is additive group of complex numbers indecomposable?

Question

Recall that a group $G$ is called indecomposable if it cannot be written as a direct sum of two proper normal subgroups.

My Question is "Is additive group of complex numbers indecomposable?

I stuck in proving this. I searched it a lot more on internet. But, I could not find any thing regarding this Question. Please give a short proof or a relevant source where I can find its solution. I will be highly thankful to you.

Now, I have added the definition of indecomposable group. Thank You for pointing it. — bipin, Mar 07 '22 at 09:10

score 1 · Accepted Answer · answered Mar 07 '22 at 09:03

1

If you mean decomposable into a direct product, then it is: it is isomorphic to $(\mathbb{R}, +) \times (\mathbb{R}, +)$.

answered Mar 07 '22 at 09:03

A. Pongrácz

7,418

Is additive group of complex numbers indecomposable?

1 Answers1