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A finite group $G$ is metabelian if its commutator subgroup is abelian. Equivalently, $G$ is an extension of an abelian group by an abelian group. Metabelian groups are solvable, and they include all abelian, dihedral, quaternion, metacyclic, extraspecial groups and groups of $p$-rank one.
Every metacylic group is metabelian, but the converse does not hold, as shown by these examples.
- Review status: reviewed
- Last edited by David Roe on 2021-10-13 23:18:41
Referred to by:History: (expand/hide all)
- 2021-10-13 23:18:41 by David Roe (Reviewed)
- 2021-10-08 14:13:49 by David Roe
- 2019-05-22 20:16:22 by Tim Dokchitser
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