GroupTheory - Maple Programming Help

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GroupTheory

 OrthogonalGroup

 Calling Sequence OrthogonalGroup(name)

Parameters

 name - : string : a name from the set { "O7(3)", "O8-(2)", "O8+(2)", "O8-(3)", "O8+(3)", "O10-(2)", "O10+(2)" }

Description

 • The orthogonal groups form a class of finite simple groups of Lie type. The OrthogonalGroup( name ) command returns a permutation group isomorphic to an orthogonal group from among those listed above.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{OrthogonalGroup}\left("O8+\left(2\right)"\right)$
 ${G}{:=}{{\mathbf{O}}}_{{8}}^{{+}}\left({2}\right)$ (1)
 > $\mathrm{Degree}\left(G\right)$
 ${120}$ (2)
 > $\mathrm{GroupOrder}\left(\mathrm{OrthogonalGroup}\left("O10-\left(2\right)"\right)\right)$
 ${25015379558400}$ (3)

Compatibility

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