Commutator properties and relative theories in communication with solvable groups

The study of groups arose from the theory equations; more specifically form the attempt to find roots of a polynomial in terms of its coefficients, early in the 19^th century. The theory of groups itself, which had already been applied in almost all branches of Mathematics, has developed in many different directions. It becomes of prime importance in many Mathematical disciplines. Here, I have studied an essential part of groups called Commutators related to solvable groups. In this study, I have discussed Commutator properties and intend to present some relative noteworthy theorems of commutators in connection with solvable groups. I have assumed the group G to be finite group throughout the whole work.