GroupTheory/IsPSoluble - Maple Help
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GroupTheory

 IsPSoluble
 attempt to determine whether a group is p-soluble

 Calling Sequence IsPSoluble( p, G )

Parameters

 p - : prime : a prime number G - : PermutationGroup : a finite permutation group

Description

 • For a prime number $p$, a finite group $G$ is $p$-soluble if it has a subnormal series every quotient of which is either a $p$-group or has order coprime to $p$.
 • Every finite soluble group is $p$-soluble for every prime number $p$.
 • The IsPSoluble( p, G ) command returns true if the group G is $p$-soluble and returns the value false if it is not.
 • The group G must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsPSoluble}\left(2,\mathrm{QuaternionGroup}\left(\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsPSoluble}\left(3,\mathrm{QuaternionGroup}\left(\right)\right)$
 ${\mathrm{true}}$ (2)
 > $G≔\mathrm{GL}\left(3,3\right):$
 > $\mathrm{map}\left(\mathrm{IsPSoluble},\left[2,3,11\right],G\right)$
 $\left[{\mathrm{false}}{,}{\mathrm{false}}{,}{\mathrm{true}}\right]$ (3)
 > $G≔\mathrm{FrobeniusGroup}\left(14520,2\right):$
 > $\mathrm{IsSoluble}\left(G\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{map}\left(\mathrm{IsPSoluble},\left[2,3,5,11\right],\mathrm{FrobeniusGroup}\left(14520,2\right)\right)$
 $\left[{\mathrm{false}}{,}{\mathrm{false}}{,}{\mathrm{false}}{,}{\mathrm{true}}\right]$ (5)
 > $\mathrm{IsPSoluble}\left(2,\mathrm{PerfectGroup}\left(936000,2\right)\right)$
 ${\mathrm{false}}$ (6)

Compatibility

 • The GroupTheory[IsPSoluble] command was introduced in Maple 2024.
 • For more information on Maple 2024 changes, see Updates in Maple 2024.

 See Also