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.
GAP 3.4.4