This paper aims at treating a study on the commutator in the group in n terms of elements for different algebraic structures as groups; subgroup and cyclic group in real numbers. After that we discuss the commutator and commutator subgroups of groups in n terms of elements which will give us a practical knowledge to see the applications. If G is a finite group and $a,b \in G$, then $C = \{ab a^{-1}b^{-1} : a,b \in G\}$ is commutator subgroup and $ab a^{-1}b^{-1}$ is the commutator of a and b. Finally, we find out the commutator in the group in n terms of elements in different types of group.