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.
GAP 3.4.4