25.7 Intersection for Ag Groups

AgGroupOps.Intersection( U, V )

If either V or U is not an ag group then GroupOps.Intersection is used in order to compute the intersection of U and V. If U and V have different parent groups then the empty list is returned.

Let U and V be two ag group with common parent group G. If one subgroup if known to be normal in G the NormalIntersection (see NormalIntersection) is used in order to compute the intersection.

If the size of U or V is smaller than GS_SIZE then the intersection is computed using GroupOps.Intersection. By default GS_SIZE is 20.

If an elementary abelian ag series of G is known, Glasby's generalized covering algorithm is used (see GS90). Otherwise a warning is given and GroupOps.Intersection is used, but this may be too slow.

    gap> d8_1 := Subgroup( s4, [ a, c, d ] );
    Subgroup( s4, [ a, c, d ] )
    gap> d8_2 := Subgroup( s4, [ a*b, c, d ] );
    Subgroup( s4, [ a*b, c, d ] )
    gap> Intersection( d8_1, d8_2 );
    Subgroup( s4, [ c, d ] )
    gap> Intersection( d8_1^b, d8_2^b );
    Subgroup( s4, [ c*d, d ] ) 

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