7.61 IsSolvable

IsSolvable( G )

IsSolvable returns true if the group G is solvable and false otherwise.

A group G is solvable if and only if the derived series of G is of finite length and reaches {1}.

Note that IsSolvable sets and tests G.isSolvable.

    gap> s4 := Group( (1,2,3,4), (1,2) );;
    gap> IsSolvable( s4 );
    true 

The default function GroupOps.IsSolvable computes the derived series using the function DerivedSeries (see DerivedSeries) in order to see whether G is solvable.

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

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