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3 Tools

3.1 Helper functions

3.1-1 PositionAndConjugatorOfStabilizer

Returns: a list with first entry an integer and second entry a group element

Returns a pair [ i, g ] such that ConjugateSubgroup( S, g ) = RepresentativeTom( ToM, i ) where S = Stabilizer( args... ) and ToM = TableOfMarks( args[1] ). See Stabilizer for a specification of args.

gap> G := SymmetricGroup( 3 );;
gap> ToM := TableOfMarks( G );;
gap> S := Stabilizer( G, 3 );
Sym( [ 1 .. 2 ] )
gap> pos_and_conj := PositionAndConjugatorOfStabilizer( G, 3 );;
gap> pos := pos_and_conj[1];
2
gap> conj := pos_and_conj[2];
(1,3)
gap> ConjugateSubgroup( S, conj ) = RepresentativeTom( ToM, pos );
true

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