IsMetacyclic - Maple Help
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GroupTheory

 IsMetacyclic
 attempt to determine whether a group is metacyclic

 Calling Sequence IsMetacyclic( G )

Parameters

 G - a finite group

Description

 • A group $G$ is metacyclic if it is an extension of a cyclic group by another cyclic group. The extension need not be proper; that is, a cyclic group is metacyclic.
 • The IsMetacyclic( G ) command attempts to determine whether the group G is metacyclic.  It returns true if G is metacyclic and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsMetacyclic}\left(\mathrm{Symm}\left(3\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsMetacyclic}\left(\mathrm{Symm}\left(4\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsMetacyclic}\left(\mathrm{MetacyclicGroup}\left(3,2,3\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsMetacyclic}\left(\mathrm{FrobeniusGroup}\left(186,1\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsMetacyclic}\left(\mathrm{CyclicGroup}\left(9\right)\right)$
 ${\mathrm{true}}$ (5)

Compatibility

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

 See Also