The commutator [a, b] of elements a and b in a group (J is defined by [a, b] =

Chapter 54, Problem 54.9

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The commutator [a, b] of elements a and b in a group (J is defined by [a, b] = a-Ib-1ab.Prove that the subgroup generated by the set of all commutators forms a normal subgroup ofG. This group is called the commutator subgroup or derived group of G, and is denoted by[G, G] orG' orGI.

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