51.3 InverseMap

InverseMap( paramap )

InverseMap( paramap )[i] is the unique preimage or the set of all preimages of i under paramap, if there are any; otherwise it is unbound.

(We have CompositionMaps( paramap, InverseMap( paramap ) ) the identity map.)

    gap> t:= CharTable( "2.A5" );; f:= CharTable( "A5" );;
    gap> fus:= GetFusionMap( t, f );    # the factor fusion map
    [ 1, 1, 2, 3, 3, 4, 4, 5, 5 ]
    gap> inverse:= InverseMap( fus );
    [ [ 1, 2 ], 3, [ 4, 5 ], [ 6, 7 ], [ 8, 9 ] ]
    gap> CompositionMaps( fus, inverse );
    [ 1, 2, 3, 4, 5 ]
    gap> t.powermap[2];
    [ 1, 1, 2, 4, 4, 8, 8, 6, 6 ]
    # transfer a powermap up to the factor group\:
    gap> CompositionMaps( fus, CompositionMaps( last, inverse ) );
    [ 1, 1, 3, 5, 4 ]                   # is equal to 'f.powermap[2]'
    # transfer a powermap down to the group\:
    gap> CompositionMaps( inverse, CompositionMaps( last, fus ) );
    [ [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 4, 5 ], [ 4, 5 ], [ 8, 9 ], 
      [ 8, 9 ], [ 6, 7 ], [ 6, 7 ] ]    # contains 't.powermap[2]'

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