54.12 TestRelativelySM

TestRelativelySM( G )
TestRelativelySM( chi, N )

If the only argument is a SM group G then TestRelativelySM returns a record with information about whether G is relatively subnormally monomial (relatively SM) with respect to every normal subgroup.

If there are two arguments, an irreducible character chi of a SM group G and a normal subgroup N of G, then TestRelativelySM returns a record with information whether chi is relatively SM with respect to N, i.e, whether there is a subnormal subgroup H of G that contains N such that chi is induced from a character psi of H where the restriction of psi to N is irreducible.

The component isRelativelySM is true or false, the component comment contains a string that describes the reason. If the argument is G, and G is not relatively SM with respect to a normal subgroup then the component character contains a not relatively SM character of such a normal subgroup.

Note: It is not checked whether G is SM.

    gap> IsSubnormallyMonomial( SolvableGroup( "A4" ) );
    #W  Warning: Group has no name
    true
    gap> TestRelativelySM( SolvableGroup( "A4" ) );
    rec(
      isRelativelySM := true,
      comment :=
       "normal subgroups are abelian or have nilpotent factor group" ) 

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