I have some difficulties with the following problem:
Let $G$ be a group with a composition serie $\mathcal G$; Let $A$ and $B$ be maximal normal subgroups of $G$; if $A'$ is a maximal normal subgroup of $A$ and $B'$ is a maximal normal subgroup of $B$ prove that $\left<A',B'\right>$ is a subnormal subgroup of $G$.
The situation is the following:
Which is the strategy to approach this problem (it is enough only a hint for the moment)? I'm looking for a solution for several days... :(
Edited: I should prove the porposition in the case "$G$ is a group (infinite order is allowed) with a composition serie... ". There is no need that $G$ is finite.