GAP Manual: 51.20. CheckFixedPoints

CheckFixedPoints( inside1, between, inside2 )

If the parametrized map (see More about Maps and Parametrized Maps) between transfers the parametrized map inside1 to inside2, i.e. inside2 circbetween = between circinside1, between must map fixed points of inside1 to fixed points of inside2. Using this property, CheckFixedPoints tries to improve between and inside2.

If an inconsistency occurs, false is returned. Otherwise, CheckFixedPoints returns the list of classes where improvements were found.

    gap> s:= CharTable( "L4(3).2_2" );; o7:= CharTable( "O7(3)" );;
    gap> fus:= InitFusion( s, o7 );;
    gap> CheckFixedPoints( s.powermap[5], fus, o7.powermap[5] );
    [ 48, 49 ]
    gap> fus:= InitFusion( s, o7 );; Sublist( fus, [ 48, 49 ] );
    [ [ 54, 55, 56, 57 ], [ 54, 55, 56, 57 ] ]
    gap> CheckFixedPoints( s.powermap[5], fus, o7.powermap[5] );
    [ 48, 49 ]
    gap> Sublist( fus, [ 48, 49 ] );
    [ [ 56, 57 ], [ 56, 57 ] ]

CheckFixedPoints is used by SubgroupFusions SubgroupFusions.