MergedCgs( U, objs )
Let U be an ag group with parent group G and objs be a list of
elements and subgroups of U. Then MergedCgs returns the subgroup S
of G generated by the elements and subgroups in the list objs. The
subgroup S contains a canonical generating system bound to S.cgs.
As objs contains only elements and subgroups of U, the subgroup S
is not only a subgroup of G but also of U. Its parent group is
nevertheless G and MergedCgs computes a canonical generating system
of S with respect to G.
If subgroups of S are known at least the largest should be an element
of objs, because MergedCgs is much faster in such cases.
Note that this function may return a wrong subgroup, if the elements of objs do not belong to U. See also Generating Systems of Ag Groups for differences between canonical and induced generating systems.
gap> d8 := MergedCgs( s4, [ a*c, c ] );
Subgroup( s4, [ a, c, d ] )
gap> MergedCgs( s4, [ a*b*c*d, d8 ] );
s4
gap> v4 := MergedCgs( d8, [ c*d, c ] );
Subgroup( s4, [ c, d ] )
GAP 3.4.4