Abstract Algebra - Normal groups

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Homework Statement



I'll be delighted to receive some guidance in the following questions:

1. Let G1,G2 be simple groups. Prove that every normal non-trivial subgroup of G= G1 x G2 is isomorphic to G1 or to G2...

2. Prove that every group of order p^2 * q where p,q are primes is solvable...

Homework Equations


The Attempt at a Solution



I've no idea about the second question. But the first one seems very easy, but I can't figure out how to solve it.


Help is needed

Thanks in advance
 

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