Assignment:
A) Prove that if H is nontrivial normal subgroup of the solvable group G then there is a nontrivial subgroup A of H with A normal subgroup of G and A abelian.
B)Prove that if there exists a chain of subgroups G1<=G2<=.....<=G such that G=union(from i=1 to infinity)of Gi and each Gi is simple, then G is simple.
Provide complete and step by step solution for the question and show calculations and use formulas.