- #1

QIsReluctant

- 37

- 3

## Homework Statement

Let G = G

_{1}× G

_{2}be the direct product of two simple groups. Prove that every normal subgroup of G is isomorphic to G, G

_{1}, G

_{2}, or the trivial subgroup.

## The Attempt at a Solution

I tried proving that the normal subgroups would have to be of the form Normal subgroup X Normal subgroup. However, that's false because, e.g., <(1,1)> is a normal subgroup of the Klein four-group.