Question:
Problems with normal subgroups
1. Let N1, ..., Nk be normal subgroups of a finite group G. If G = N1N2 ...Nk (the set of all elements of the form a1a2...ak with a j in N j) and |G| = |N1| . |N2| . |N3| ... |Nk|, prove that G = N1 x N2 x N3 x ... x Nk.