25.82 IntersectionSumAgGroup

IntersectionSumAgGroup( V, W )

Let V and W be ag groups with a common parent group, such that <W> leq N (<V>). Then <V> * <W> is a subgroup and IntersectionSumAgGroup returns the intersection and the sum of V and W as record R with components R.intersection and R.sum.

The function uses the Zassenhaus sum-intersection algorithm. See also NormalIntersection and SumAgGroup. For more information about the Zassenhaus algorithm see ExtendedIntersectionSumAgGroup and SumFactorizationFunctionAgGroup.

Note that this functions returns an incorrect result if <W> not leq N(<V>).

    gap> d8_1 := AgSubgroup( s4, [ a, c, d ], true );
    Subgroup( s4, [ a, c, d ] )
    gap> d8_2 := AgSubgroup( s4, [ a*b, c, d ], true );
    Subgroup( s4, [ a*b, c, d ] )
    gap> IntersectionSumAgGroup( d8_1, d8_2 );
    rec(
      sum := Group( a*b, b^2, c, d ),
      intersection := Subgroup( s4, [ c, d ] ) ) 

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