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> circ <between> = <between> circ <inside1>,
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
.
GAP 3.4.4