Why G(P/F) and G(Q/F) abelian implies PQ abelian?

26 Views Asked by At

Suppose L/F is a field extension, then L/P/F with P/F abelian and L/Q/F with Q/F abelian implies PQ=P(Q) abelian.

After trying to pick element from PQ, I still can't find the relation between PQ and the fact that G(P/F) and G(Q/F) are abelian.