7.57 IsNilpotent

IsNilpotent( G )

IsNilpotent returns true if the group G is nilpotent and false otherwise.

A group G is nilpotent if and only if the lower central series of G is of finite length and reaches {1}.

Note that IsNilpotent sets and tests the record component G.isNilpotent.

    gap> s4 := Group( (1,2,3,4), (1,2) );;
    gap> IsNilpotent( s4 );
    false
    gap> v4 := Group( (1,2)(3,4), (1,3)(2,4) );;
    gap> IsNilpotent( v4 );
    true 

The default group function GroupOps.IsNilpotent computes the lower central series using LowerCentralSeries (see LowerCentralSeries) in order to check whether G is nilpotent.

If G has an infinite set of elements a warning is given, as this function does not stop if G has a lower central series of infinite length.

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