Examples where $G \cong G \times H$ where $H$ is nontrivial?

Question

I am new to abstract algebra and ran into the problem yesterday. With my rudimentary knowledge of set theory I can deduce $G$ must be infinite, but I cannot move on any further. One example I can think of is the infinite direct product of some group $G$. I am wondering if there is any other easily understandable example?

I haven't looked closely, but it's possible that this related question will have an example, although the condition it is asking for is weaker than yours: Does $G\cong G/H$ imply that $H$ is trivial? — MJD, Nov 18 '16 at 19:29

score 0 · Answer 1 · answered Nov 18 '16 at 23:38

0

If G=U^(omega) and H is U where U is a group. Although that might be what you were talking about in the question.

answered Nov 18 '16 at 23:38

Jacob Wakem

2,382

Examples where $G \cong G \times H$ where $H$ is nontrivial?

1 Answers1