GroupTheory - Maple Programming Help

Home : Support : Online Help : Mathematics : Group Theory : GroupTheory package : GroupTheory/HeldGroup

GroupTheory

 HeldGroup

 Calling Sequence HeldGroup()

Description

 • The Held group of order $4030387200$ is one of the sporadic finite simple groups. It was discovered by Dieter Held in 1969 as a group containing an involution whose centralizer is isomorphic to the centralizer of an involution in the Mathieu group ${M}_{24}$.  (The only other such group is the group $PSL\left(5,2\right)$ .) The construction of the Held group was later completed by Graham Higman and John McKay. The Held group can also be realized as the centralizer of an element of order $7$ in the Monster.
 • The HeldGroup() command returns either a permutation group, or a finitely presented group, isomorphic to the Held group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{HeldGroup}\left(\right)$
 ${G}{≔}{\mathbf{He}}$ (1)
 > $\mathrm{Degree}\left(G\right)$
 ${2058}$ (2)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${4030387200}$ (3)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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