69.5 AbelianComponent

AbelianComponent( QUOT )

This function takes as input the output of a CallPCQA function call (see CallPCQA) or an ExtendPCQA function call (see ExtendPCQA) and returns the structure of the abelian groups which appear as quotients in the derived series. The structure of each of these quotients is given by an array of nonnegative integers.Read the section on ElementaryDivisors for details.

    gap> F := FreeGroup(3);
    Group( f.1, f.2, f.3 )
    gap> G := F/[F.1*F.2*F.1*F.2,F.2*F.3^2*F.2*F.3,F.3^6];
    Group( f.1, f.2, f.3 )
    gap> quot := CallPCQA(G,2);;
    gap> AbelianComponent(quot);
    [ [ 1, 2, 12 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ]

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