Prove that any infinite abelian group G does not have a composition series.
(HINT: Suppose it does and come to a contradiction. Also use the result of exercise 4 for Section 6.3.)
Prove that a finite group is solvable if and only if the factors of a composition series are cyclic groups having prime orders.
Prove that if is a group which has a composition series, then any normal subgroup of and any factor group of also have composition series with factors isomorphic to composition factors of .