IsMetabelian - Maple Help
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GroupTheory

 IsMetabelian
 attempt to determine whether a group is metabelian

 Calling Sequence IsMetabelian( G )

Parameters

 G - a group

Description

 • A group $G$ is metabelian if it is an extension of an Abelian group by another Abelian group.  Equivalently, $G$ is metabelian if its derived subgroup is Abelian. Note that every abelian group is metabelian.
 • The IsMetabelian( G ) command attempts to determine whether the group G is metabelian.  It returns true if G is metabelian and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsMetabelian}\left(\mathrm{Symm}\left(4\right)\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{IsMetabelian}\left(\mathrm{Alt}\left(4\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{IsMetabelian}\left(\mathrm{FrobeniusGroup}\left(600,1\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsMetabelian}\left(\mathrm{FrobeniusGroup}\left(600,2\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsMetabelian}\left(\mathrm{ElementaryGroup}\left(5,5\right)\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{IsMetabelian}\left(\mathrm{QuasicyclicGroup}\left(13\right)\right)$
 ${\mathrm{true}}$ (6)

Compatibility

 • The GroupTheory[IsMetabelian] command was introduced in Maple 2019.
 • For more information on Maple 2019 changes, see Updates in Maple 2019.
 • The GroupTheory[IsMetabelian] command was updated in Maple 2023.