Complete groups or derived groups

Complete Group:

if the centre 𝜁( G) of a group 𝐺 is trevial and very automorphism of 𝐺 is an inner

automorphism, 𝐺 is called a complete group

Derived Group OR Commutator Subgroup:

Let 𝐺 be a group and 𝐺′ be a subgroup of 𝐺. Then 𝐺′is said to be a commutator subgroup, if it is generated by a set of commutators of 𝐺.

Simple group :

A group is said to be simple group if it has no proper normal subgroups.

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