7.60 IsSimple

IsSimple( G )

IsSimple returns true if G is simple and false otherwise.

A group G is simple if and only if G and the trivial subgroup are the only normal subgroups of G.

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> IsSimple( DerivedSubgroup( s4 ) );
    false
    gap> s5 := Group( (1,2,3,4,5), (1,2) );
    Group( (1,2,3,4,5), (1,2) )
    gap> IsSimple( DerivedSubgroup( s5 ) );
    true 

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