LyonsGroup - Maple Help

GroupTheory

 LyonsGroup

 Calling Sequence LyonsGroup()

Description

 • The Lyons group of order $51765179004000000$ is one of the sporadic finite simple groups.  It is among the so-called pariahs, not being a subquotient of the Monster.  The existence and uniqueness of this group was proved by Charles Sims in 1973, but its existence had been predicted earlier by Richard Lyons.  Therefore, it is sometimes called the Lyons-Sims group.
 • The LyonsGroup() command returns a symbolic representation of the Lyons simple group.
 • In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{LyonsGroup}\left(\right)$
 ${G}{≔}{\mathbf{Ly}}$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${51765179004000000}$ (2)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (3)

Compatibility

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