7.44 UpperCentralSeries

UpperCentralSeries( G )

UpperCentralSeries returns the upper central series of G as a list of subgroups.

The upper central series is the series S_n, ..., S_0 defined by S_0 = {1} < <G> and S_i/S_{i-1} = Z( <G>/S_{i-1} ) where n = min{ i ; S_i = S_{i+1} }

Note that this function may not terminate if G is an infinite group. UpperCentralSeries sets and tests G.upperCentralSeries in the group record of G.

    gap> d8 := AgGroup( Group( (1,2,3,4), (1,2)(3,4) ) );
    Group( g1, g2, g3 )
    gap> UpperCentralSeries( d8 );
    [ Group( g1, g2, g3 ), Subgroup( Group( g1, g2, g3 ), [ g3 ] ), 
      Subgroup( Group( g1, g2, g3 ), [  ] ) ] 

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