LowerCentralSeries( G )
LowerCentralSeries
returns the lower central series of G as a list of
group records.
The lower central series is the series defined by S_1 = <G> and S_i = [ <G>, S_{i-1} ]. The group G is nilpotent if this series reaches {1} after finitely many steps.
Note that this function may not terminate if G is an infinite group.
LowerCentralSeries
sets and tests the record component
G.lowerCentralSeries
in the group record of G.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> LowerCentralSeries( s4 ); [ Group( (1,2,3,4), (1,2) ), Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,3,2), (2,4,3) ] ) ]
The default group function GroupOps.LowerCentralSeries
uses
CommutatorSubgroup
(see CommutatorSubgroup) in order to compute the
lower central series of G.
GAP 3.4.4