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           1.The group G is said to be solvable if there exists a finite chain of subgroups
               G = N0 N1 · · · Nn such that

(i) Ni is a normal subgroup in Ni-1 for i = 1,2, . . . ,n,
(ii) Ni-1 / Ni is abelian for i = 1,2, . . . ,n, and
(iii) Nn = {e}.

2. A finite group G is solvable if and only if there exists a finite chain of subgroups
G = N0 N1 · · · Nn such that
(i) Ni is a normal subgroup in Ni-1 for i = 1,2, . . . ,n,
(ii) Ni-1 / Ni is cyclic of prime order for i = 1,2, . . . ,n, and
(iii) Nn = {e}.

3.Let p be a prime number. Any finite p-group is solvable.

4. The symmetric group Sn is not solvable for n 5.

5. Every subgroup of a solvable group is solvable.

6. Every quotient group of a solvable group is solvable.