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## Homework Statement

This is an exercise from Jacobson Algebra I, which has me stumped.

Let G = G1 x G2 be a group, where G1 and G2 are simple groups.

Prove that every proper normal subgroup K of G is isomorphic to G1 or G2.

## Homework Equations

## The Attempt at a Solution

Certainly the intersection of K with G1 x {1} is normal, and so is isomorphic to the trivial group {1} or to G1. Similarly, the intersection of K with {1} x G2 is isomorphic to {1} or G2. But anyway this falls well short of a solution.

Thanks,

John