PCore - Maple Help

GroupTheory

 PCore
 construct the p-core of a group

 Calling Sequence PCore( p, G )

Parameters

 p - prime number G - a permutation group

Description

 • The $p$-core of a group $G$ is the largest normal $p$-subgroup of $G$, where $p$ is a prime integer.  It is equal to the intersection of the Sylow $p$-subgroups of $G$, which is, in turn, equal to the core of any one Sylow $p$-subgroup.
 • The PCore( p, G ) command constructs the p-core of a group G. The group G must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{DihedralGroup}\left(14\right)$
 ${G}{≔}{{\mathbf{D}}}_{{14}}$ (1)
 > $C≔\mathrm{PCore}\left(2,G\right)$
 ${C}{≔}{{O}}_{{2}}{}\left({{\mathbf{D}}}_{{14}}\right)$ (2)
 > $\mathrm{GroupOrder}\left(C\right)$
 ${2}$ (3)
 > $\mathrm{GroupOrder}\left(\mathrm{SylowSubgroup}\left(2,G\right)\right)$
 ${4}$ (4)
 > $C≔\mathrm{PCore}\left(7,G\right)$
 ${C}{≔}{{O}}_{{7}}{}\left({{\mathbf{D}}}_{{14}}\right)$ (5)
 > $\mathrm{GroupOrder}\left(C\right)$
 ${7}$ (6)

Compatibility

 • The GroupTheory[PCore] command was introduced in Maple 17.