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
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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