70.3 IsCompatiblePCentralSeries

IsCompatiblePCentralSeries( G )

If the component G.isCompatiblePCentralSeries of the polycyclically presented p-group G is bound, its value is returned, otherwise the exponent-p-central series of G is computed and compared to the given presentation. If the generators of each term of this series form a subset of the generators of G the component G.isCompatiblePCentralSeries is set to true, otherwise to false. This value is then returned by the function.

    gap> g:= SolvableGroup( "D8" );;
    gap> IsCompatiblePCentralSeries ( g );
    true
    gap> a := AbstractGenerators ( "a", 5 );;
    gap> h := AgGroupFpGroup ( rec (
    > generators := a,
    > relators := 
    > [a[1]^2/(a[3]*a[5]),a[2]^2/a[3],a[3]^2/(a[4]*a[5]),a[4]^2,a[5]^2]));;
    gap> h.name := "H";;
    gap> IsCompatiblePCentralSeries ( h );
    false
    gap> PCentralSeries ( h, 2 );
    [ H, Subgroup( H, [ a3, a4, a5 ] ), Subgroup( H, [ a4*a5 ] ), 
      Subgroup( H, [  ] ) ] 

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