54.9 TestSubnormallyMonomial

TestSubnormallyMonomial( G )
TestSubnormallyMonomial( chi )

returns a record with information whether the group G or the irreducible group character chi of the group G is subnormally monomial.

The result contains the components

isSubnormallyMonomial:

true or false,

comment:

a string telling a reason for the value of the isSubnormallyMonomial component,

character:

if bound, a character of G that is not subnormally monomial.

IsSubnormallyMonomial( G ) IsSubnormallyMonomial( chi )

returns true if the group G or the group character chi is subnormally monomial, and false otherwise.

    gap> TestSubnormallyMonomial( S4 );
    rec(
      isSubnormallyMonomial := false,
      character := Character( S4, [ 3, -1, 0, -1, 1 ] ),
      comment := "found not SM character" )
    gap> TestSubnormallyMonomial( Irr( S4 )[4] );
    rec(
      isSubnormallyMonomial := false,
      comment := "all subnormal subgroups checked" )
    gap> TestSubnormallyMonomial( SolvableGroup( "A4" ) );
    #W  Warning: Group has no name
    rec(
      isSubnormallyMonomial := true,
      comment := "all irreducibles checked" ) 

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