Let us recall that a group $G$ is called *perfect* if it coincides with its commutator subgroup $G'$, or equivalently, if its abelianization $G/G'$ is trivial.



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> **Question.** Is there any name for a group $G$ whose abelianization $G/G'$ is finite?
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A name for a group with finite abelization?
Prompted by the OP, I'm writing my comment as an answer.


I suggest “almost perfect” group. A google search indicates this terminology has been used; for instance, here: core.ac.uk/download/pdf/61487184.pdf .


