7.39 ElementaryAbelianSeries

ElementaryAbelianSeries( G )

Let G be a solvable group (see IsSolvable). Then the functions returns a normal series G = E_0, E_1, ..., E_n = {1} of G such that the factor groups E_i / E_{i+1} are elementary abelian groups.

    gap> s5 := SymmetricGroup( 5 );; s5.name := "s5";;
    gap> s4 := Subgroup( s5, [ (2,3,4,5), (2,3) ] );
    Subgroup( s5, [ (2,3,4,5), (2,3) ] )
    gap> ElementaryAbelianSeries( s4 );
    [ Subgroup( s5, [ (2,3), (2,4,3), (2,5)(3,4), (2,3)(4,5) ] ),
      Subgroup( s5, [ (2,4,3), (2,5)(3,4), (2,3)(4,5) ] ),
      Subgroup( s5, [ (2,5)(3,4), (2,3)(4,5) ] ), Subgroup( s5, [  ] ) ] 

The default function GroupOps.ElementaryAbelianSeries uses AgGroup (see AgGroup) in order to convert G into an isomorphic ag group and computes the elementary abelian series in this group. (see Group Functions for Ag Groups).

Previous Up Top Next
Index