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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A ctblmono.xml GAP documentation Thomas Breuer -->
<!-- %A & Erzsébet Horváth -->
<!-- %% -->
<!-- %% -->
<!-- %Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<Chapter Label="Monomiality Questions">
<Heading>Monomiality Questions</Heading>
This chapter describes functions dealing with the monomiality
of finite (solvable) groups and their characters.
<P/>
<#Include Label="[1]{ctblmono}">
<P/>
Several <E>examples</E> in this chapter use the symmetric group <M>S_4</M>
and the special linear group <M>SL(2,3)</M>.
For running the examples, you must first define the groups,
for example as follows.
<P/>
<Example><![CDATA[
gap> S4:= SymmetricGroup( 4 );; SetName( S4, "S4" );
gap> Sl23:= SL( 2, 3 );;
]]></Example>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sect:InfoMonomial">
<Heading>InfoMonomial (Info Class)</Heading>
<#Include Label="InfoMonomial">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Character Degrees and Derived Length">
<Heading>Character Degrees and Derived Length</Heading>
<#Include Label="Alpha">
<#Include Label="Delta">
<#Include Label="IsBergerCondition">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Primitivity of Characters">
<Heading>Primitivity of Characters</Heading>
<#Include Label="TestHomogeneous">
<#Include Label="IsPrimitiveCharacter">
<#Include Label="TestQuasiPrimitive">
<#Include Label="TestInducedFromNormalSubgroup">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Testing Monomiality">
<Heading>Testing Monomiality</Heading>
<#Include Label="[2]{ctblmono}">
<#Include Label="TestMonomial">
<#Include Label="TestMonomialUseLattice">
<#Include Label="IsMonomialNumber">
<#Include Label="TestMonomialQuick">
<#Include Label="TestSubnormallyMonomial">
<#Include Label="TestRelativelySM">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Minimal Nonmonomial Groups">
<Heading>Minimal Nonmonomial Groups</Heading>
<#Include Label="IsMinimalNonmonomial">
<#Include Label="MinimalNonmonomialGroup">
</Section>
</Chapter>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->
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