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The Group Theory package includes an extensive collection of routines for constructing, computing with, and visualizing finitely generated groups, including permutation groups, finitely presented groups, Cayley table groups, “black-box” user defined groups, and abstract groups depending on symbolic parameters. Several new commands have been added to the Group Theory package in Maple 2018 for performing new tests and calculating more properties.
> | with( GroupTheory ): |
> | G := Symm( 4 ); |
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> | H := Subgroup( { Perm( [[1,2],[3,4]] ) }, G ); |
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> | IsSubnormal( H, G ); |
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> | IsPermutable( H, G ); |
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> | IsNormal( H, G ); |
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> | G := Symm( 3 ); |
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> | N := Subgroup( { Perm( [[1,2,3]] ) }, G ); |
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> | IsNormal( N, G ); |
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> | IsPermutable( N, G ); |
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> | IsSubnormal( N, G ); |
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> | IsPGroup( Symm( 3 ) ); |
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> | IsPGroup( DihedralGroup( 4 ) ); |
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> | PGroupPrime( DihedralGroup( 4 ) ); |
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> | IsPGroup( DirectProduct( CyclicGroup( 128 ), QuaternionGroup() ) ); |
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> | G := < a, b | a^2, b^3, (a.b)^5 = 1 >: |
> | ElementOrder( a.b^2 .a, G ); |
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> | ClassNumber( Symm( 3 ) ); |
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> | ClassNumber( DirectProduct( Monster(), DihedralGroup( 4 * n ) ) ) assuming n :: posint; |
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> | NumAbelianGroups( 1000 ); |
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