7.41 LowerCentralSeries

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.

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GAP 3.4.4
April 1997