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A group is $G$ perfect if $G=G'$, that is if its commutator subgroup is the whole group. This is the same as to say that $G$ has no non-trivial cyclic (equivalently abelian, equivalently soluble) quotients. All non-abelian simple and quasisimple groups are perfect. A perfect group may have cyclic composition factors, for example SL$_2(\mathbb{F}5)=C_2.A_5$ is perfect.

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• Review status: beta
• Last edited by Meow Wolf on 2019-05-22 11:47:53
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