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, [ ] ) ]
GAP 3.4.4