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 Jennifer Paulhus on 2022-07-18 16:01:32
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- columns.gps_groups.perfect
- columns.gps_subgroups.perfect
- group.properties_interdependencies
- group.quasisimple
- group.stem_extension
- lmfdb/groups/abstract/main.py (lines 230-231)
- lmfdb/groups/abstract/main.py (line 398)
- lmfdb/groups/abstract/main.py (line 917)
- lmfdb/groups/abstract/main.py (line 1576)
- lmfdb/groups/abstract/main.py (line 1751)
- 2022-07-18 16:01:32 by Jennifer Paulhus (Reviewed)
- 2021-10-13 11:07:39 by David Roe
- 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