7.37 DerivedSeries

DerivedSeries( G )

DerivedSeries returns the derived series of G.

The derived series is the series of iterated derived subgroups. The group G is solvable if and only if this series reaches {1} after finitely many steps.

Note that this function does not terminate if G is an infinite group with derived series of infinite length.

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> DerivedSeries( s4 );
    [ Group( (1,2,3,4), (1,2) ), Subgroup( Group( (1,2,3,4), (1,2) ), 
        [ (1,3,2), (1,4,3) ] ), Subgroup( Group( (1,2,3,4), (1,2) ), 
        [ (1,4)(2,3), (1,3)(2,4) ] ), 
      Subgroup( Group( (1,2,3,4), (1,2) ), [  ] ) ] 

The default function GroupOps.DerivedSeries uses DerivedSubgroup (see DerivedSubgroup) in order to compute the derived series of G.

Previous Up Top Next
Index