7.59 IsPerfect

IsPerfect( G )

IsPerfect returns true if G is a perfect group and false otherwise.

A group G is perfect if G is equal to its derived subgroup. See DerivedSubgroup.

Note that IsPerfect sets and tests G.isPerfect.

    gap> a4 := Group( (1,2,3), (2,3,4) );
    Group( (1,2,3), (2,3,4) )
    gap> IsPerfect( a4 );
    false
    gap> a5 := Group( (1,2,3), (2,3,4), (3,4,5) );
    Group( (1,2,3), (2,3,4), (3,4,5) )
    gap> IsPerfect( a5 );
    true 

The default group function GroupOps.IsPerfect checks for a finite group G the index of <G>^prime (see DerivedSubgroup) in G. For an infinite group it computes the abelian invariants of the commutator factor group (see AbelianInvariants and CommutatorFactorGroup).

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