25.58 FactorGroup for AgGroups

AgGroupOps.FactorGroup( U, N )

Let N and U be ag groups with a common parent group, such that N is a normal subgroup of U. Let H be the factor group <U> / <N>. FactorGroup returns the finite polycyclic group H as new parent group.

If the ag group U is not a parent group or if N is not an element of the AG series of U (see IsElementAgSeries), then FactorGroup constructs a new polycyclic presentation and collector for the factor group using both FpGroup (see FpGroup for Ag Groups) and AgGroupFpGroup (see AgGroupFpGroup). Otherwise FactorGroup copies the old collector of U and cuts of the tails which lie in N.

Note that N must be a normal subgroup of U. You should keep in mind, that although the new generators and the old ones may have the same names, they cannot be multiplitied as they are elements of different groups. The only way to transfer information back and forth is to use the homomorphisms returned by NaturalHomomorphism (see FactorGroup).

    gap> c2 := Subgroup( s4, [ d ] );
    Subgroup( s4, [ d ] )
    gap> d8 := Subgroup( s4, [ a, c, d ] );
    Subgroup( s4, [ a, c, d ] )
    gap> v4 := FactorGroup( d8, c2 );
    Group( g1, g2 )
    gap> v4.2 ^ v4.1;
    g2
    gap> d8 := Subgroup( s4, [ a, c, d ] );
    Subgroup( s4, [ a, c, d ] )
    gap> d8.2^d8.1;
    c*d 

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