7.23 FittingSubgroup

FittingSubgroup( G )

FittingSubgroup returns the Fitting subgroup of G.

The Fitting subgroup of a group G is the biggest nilpotent normal subgroup of G.

    gap> s4;
    Group( (1,2,3,4), (1,2) )
    gap> FittingSubgroup( s4 );
    Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,3)(2,4), (1,4)(2,3) ] )
    gap> IsNilpotent( last );
    true 

Let G be a finite group. Then the default group function GroupOps.FittingSubgroup computes the subgroup of G generated by the cores of the Sylow subgroups in G.

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