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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A gptransv.xml GAP documentation Gene Cooperman -->
<!-- %A and Scott Murray -->
<!-- %% -->
<!-- %% -->
<!-- %Y (C) 2000 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<Chapter Label="Transversals of subgroups">
<Heading>Transversals of subgroups (preliminary)</Heading>
<#Include Label="[1]{gptransv}">
<P/>
<E>The functions and operations described in this chapter have been added
very recently and are still undergoing development. It is conceivable that
names of variants of the functionality might change in future versions. If
you plan to use these functions in your own code, please contact us.</E>
<P/>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="General operations on transversals">
<Heading>General operations on transversals</Heading>
<#Include Label="[2]{gptransv}">
<P/>
<#Include Label="TransversalElt">
<#Include Label="SiftOneLevel">[gptransv]!{for subgroup transversals}
<P/>
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Transversals by Schreier tree">
<Heading>Transversals by Schreier tree</Heading>
<#Include Label="[3]{gptransv}">
<P/>
<#Include Label="SchreierTransversal">
<#Include Label="OrbitGenerators">
<#Include Label="OrbitGeneratorsInv">
<#Include Label="BasePointOfSchreierTransversal">
<#Include Label="One">
<#Include Label="ExtendSchreierTransversal">
<#Include Label="ExtendSchreierTransversalShortCube">
<#Include Label="ExtendSchreierTransversalShortTree">
<#Include Label="CompleteSchreierTransversal">
<#Include Label="PreferredGenerators">
<#Include Label="SchreierTreeDepth">
<P/>
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Transversals by homomorphic images">
<Heading>Transversals by homomorphic images</Heading>
<#Include Label="[4]{gptransv}">
<P/>
<#Include Label="HomTransversal">
<#Include Label="Homomorphism">[gptransv]!{for subgroup transversals}
<#Include Label="QuotientGroup">
<#Include Label="ImageGroup">
<P/>
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Transversals by direct products">
<Heading>Transversals by direct products</Heading>
<#Include Label="[5]{gptransv}">
<P/>
<#Include Label="Projection">
<#Include Label="Injection">
<P/>
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Transversals by Trivial subgroups">
<Heading>Transversals by Trivial subgroups</Heading>
<#Include Label="[6]{gptransv}">
<P/>
<#Include Label="TransversalByTrivial">
<P/>
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Transversals by sift functions">
<Heading>Transversals by sift functions</Heading>
<#Include Label="[7]{gptransv}">
<P/>
<#Include Label="TransversalBySiftFunction">
<P/>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->
<P/>
</Section>
</Chapter>
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