This chapter describes functions dealing with monomiality questions.
Section More about Monomiality Questions gives some hints how to use the functions in the package.
The next sections (see Alpha, Delta, BergerCondition) describe functions that deal with character degrees and derived length.
The next sections describe tests for homogeneous restriction, quasiprimitivity, and induction from a normal subgroup of a group character (see TestHomogeneous, TestQuasiPrimitive, IsPrimitive for Characters, TestInducedFromNormalSubgroup).
The next sections describe tests for subnormally monomiality, monomiality, and relatively subnormally monomiality of a group or group character (see TestSubnormallyMonomial, TestMonomialQuick, TestMonomial, TestRelativelySM).
The final sections IsMinimalNonmonomial and MinimalNonmonomialGroup describe functions that construct minimal nonmonomial groups, or check whether a group is minimal nonmonomial.
All examples in this chapter use the symmetric group S_4 and the special linear group Sl(2,3). For running the examples, you must first define the groups.
gap> S4:= SolvableGroup( "S4" );; gap> Sl23:= SolvableGroup( "Sl(2,3)" );;