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