53.12 InertiaSubgroup

InertiaSubgroup( G, chi )

For a class function chi of a normal subgroup N of the group G, InertiaSubgroup( G, chi ) returns the inertia subgroup I_G(<chi>), that is, the subgroup of all those elements g in <G> that satisfy <chi> ^ g = <chi>.

    gap> V4:= Subgroup( S4, S4.generators{ [ 3, 4 ] } );
    Subgroup( S4, [ c, d ] )
    gap> irrsub:= Irr( V4 );
    #W  Warning: Group has no name
    [ Character( Subgroup( S4, [ c, d ] ), [ 1, 1, 1, 1 ] ), 
      Character( Subgroup( S4, [ c, d ] ), [ 1, 1, -1, -1 ] ), 
      Character( Subgroup( S4, [ c, d ] ), [ 1, -1, 1, -1 ] ), 
      Character( Subgroup( S4, [ c, d ] ), [ 1, -1, -1, 1 ] ) ]
    gap> List( irrsub, x -> InertiaSubgroup( S4, x ) );
    [ Subgroup( S4, [ a, b, c, d ] ), Subgroup( S4, [ a*b^2, c, d ] ),
      Subgroup( S4, [ a*b, c, d ] ), Subgroup( S4, [ a, c, d ] ) ] 

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