A group $G$ is **perfect** if it is equal to its own commutator subgroup $G'$. Equivalently, $G$ 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, $\mathrm{SL}(2,5)=C_2.A_5$ is perfect.

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- Last edited by Manami Roy on 2020-12-06 11:24:05

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- 2020-12-06 11:24:05 by Manami Roy
- 2020-12-06 11:19:52 by Manami Roy
- 2019-05-22 11:47:53 by Tim Dokchitser
- 2019-05-22 11:44:51 by Tim Dokchitser

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