7.34 FactorGroupElement

FactorGroupElement( N, g )

FactorGroupElement returns the coset N * g as a group element. It is not tested whether g normalizes N, but g must be an element of the parent group of N.

Factor group elements returned by FactorGroupElement are represented by records. Those records contain the following components.

isGroupElement:

contains true.

isFactorGroupElement:

contains true.

element:

contains a right coset of N (see RightCoset).

domain:

contains FactorGroupElements (see Domain).

operations:

contains the operations record FactorGroupElementOps.

All operations for group elements (see Operations for Group Elements) are available for factor group elements, e.g., two factor group elements can be multiplied (provided that they have the same subgroup N).

    gap> a4 := Group( (1,2,3), (2,3,4) );;  a4.name := "a4";;
    gap> v4 := Subgroup(a4,[(1,2)(3,4),(1,3)(2,4)]);;  v4.name := "v4";;
    gap> x := FactorGroupElement( v4, (1,2,3) );
    FactorGroupElement( v4, (2,4,3) )
    gap> y := FactorGroupElement( v4, (2,3,4) );
    FactorGroupElement( v4, (2,3,4) )
    gap> x * y;
    FactorGroupElement( v4, () ) 

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