7.38 CompositionSeries

CompositionSeries( G )

CompositionSeries returns a composition series of G as list of subgroups.

    gap> s4 := SymmetricGroup( 4 );
    Group( (1,4), (2,4), (3,4) )
    gap> s4.name := "s4";;
    gap> CompositionSeries( s4 );
    [ Subgroup( s4, [ (1,2), (1,3,2), (1,3)(2,4), (1,2)(3,4) ] ),
      Subgroup( s4, [ (1,3,2), (1,3)(2,4), (1,2)(3,4) ] ),
      Subgroup( s4, [ (1,3)(2,4), (1,2)(3,4) ] ),
      Subgroup( s4, [ (1,2)(3,4) ] ), Subgroup( s4, [  ] ) ]
    gap> d8 := SylowSubgroup( s4, 2 );
    Subgroup( s4, [ (1,2), (3,4), (1,3)(2,4) ] )
    gap> CompositionSeries( d8 );
    [ Subgroup( s4, [ (1,3)(2,4), (1,2), (3,4) ] ),
      Subgroup( s4, [ (1,2), (3,4) ] ), Subgroup( s4, [ (3,4) ] ),
      Subgroup( s4, [  ] ) ] 

Note that there is no default function. GroupOps.CompositionSeries signals an error if called.

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