25.84 SumFactorizationFunctionAgGroup

SumFactorizationFunctionAgGroup( U, N )

Let U and N be ag group with a common parent group such that U normalizes N. Then the function returns a record R with the following components.

intersection:

is bound to the intersection <U> cap <N>.

sum:

is bound to the sum <U> * <N>.

factorization:

is bound to function, which takes an element g of <U> * <N> and returns the factorization of g in an element u of U and n of N, such that g = u {*} n. This factorization is returned as record r with components r.u and r.n, where r.u is bound to the ag word u, r.n to the ag word n.

Note that N must be a normal subgroup of <U> * <N>, it is not sufficient that <U> * <N> = <N> * <U>.

    gap> v4 := AgSubgroup( s4, [ a*b, c ], true );
    Subgroup( s4, [ a*b, c ] )
    gap> a4 := AgSubgroup( s4, [ b, c, d ], true );
    Subgroup( s4, [ b, c, d ] )
    gap> sd := SumFactorizationFunctionAgGroup;
    function ( U, N ) ... end
    gap> sd := SumFactorizationFunctionAgGroup( v4, a4 );
    rec(
      sum := Group( a*b, b, c, d ),
      intersection := Subgroup( s4, [ c ] ),
      factorization := function ( un ) ... end )
    gap> sd.factorization( a*b*c*d );
    rec(
      u := a*b*c,
      n := d )
    gap> sd.factorization( a*b^2*c*d );
    rec(
      u := a*b*c,
      n := b*c ) 

Previous Up Top Next
Index