7.42 PCentralSeries

PCentralSeries( G, p )

PCentralSeries returns the p-central series of a group G for a prime p.

The p-central series of a group G is defined as follows. S_1 = G and S_{i+1} is set to [G,S_i] * S_i^p. The length of this series is n, where n = max{ i ; S_i > S_{i+1} }.

    gap> s4 := Group( (1,2,3,4), (1,2) );; s4.name := "s4";;
    gap> PCentralSeries( s4, 3 );
    [ s4 ]
    gap> PCentralSeries( s4, 2 );
    [ s4, Subgroup( s4, [ (1,2,3), (1,3,4) ] ) ] 

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