TestMonomial( chi )
TestMonomial( G )
returns a record containing information about monomiality of the group G or the group character chi of a solvable group, respectively.
If a character chi is proved to be monomial the result contains
comment (a string telling a
reason for monomiality), and if it was necessary to compute a linear
character from that chi is induced, also a component
If chi or G is proved to be nonmonomial the component
false, and in the case of G a nonmonomial character is contained
in the component
character if it had been necessary to compute it.
If the program cannot prove or disprove monomiality then the result
record contains the component
isMonomial with value
This case occurs in the call for a character chi if and only if chi is not induced from the inertia subgroup of a component of any reducible restriction to a normal subgroup. It can happen that chi is monomial in this situation.
For a group this case occurs if no irreducible character can be proved to be nonmonomial, and if no decision is possible for at least one irreducible character.
IsMonomial( G )
IsMonomial( chi )
true if the group G or the character chi of a solvable group
can be proved to be monomial,
false if it can be proved to be nonmonomial,
and the string
gap> TestMonomial( S4 ); rec( isMonomial := true, comment := "abelian by supersolvable group" ) gap> TestMonomial( Sl23 ); rec( isMonomial := false, comment := "list Delta( G ) contains entry > 1" )
IsMonomial( n )
for a positive integer n returns
true if every solvable group of order
n is monomial, and
gap> Filtered( [ 1 .. 111 ], x -> not IsMonomial( x ) ); [ 24, 48, 72, 96, 108 ]
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