25.60 FactorArg

FactorArg( U, N )

Let N be a normal subgroup of an ag group U. Then FactorArg returns a record with the following components with can be used as argument for Exponents.

isFactorArg:

is true.

factorNum:

contains U.

factorDen:

contains N.

identity:

contains the identity of U.

generators:

contains a list of those induced generators u_i of U of depth d_i such that no induced generator in N has depth d_i.

operations:

contains the operations record FactorArgOps.

Note that FactorArg is bound to AgGroupOps.mod.

    gap> d8 := Subgroup( s4, [ a, c, d ] );
    Subgroup( s4, [ a, c, d ] )
    gap> c2 := Subgroup( s4, [ d ] );
    Subgroup( s4, [ d ] )
    gap> M := d8 mod c2;;
    gap> d8.1 * d8.2 * d8.3;
    a*c*d
    gap> Exponents( M, last );
    [ 1, 1 ]
    gap> d8 := AgSubgroup( s4, [ a*c, c, d ], false );
    Subgroup( s4, [ a*c, c, d ] )
    gap> M := d8 mod c2;;
    gap> Exponents( M, a*c*d );
    [ 1, 0 ] 

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