<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A  grpchain.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="Chains of subgroups">
<Heading>Chains of subgroups (preliminary)</Heading>

<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/>
<#Include Label="[1]{grpchain}">
<P/>
<#Include Label="IsChainTypeGroup">
<P/>
<#Include Label="ChainSubgroup">
<#Include Label="Transversal">
<#Include Label="IsInChain">
<#Include Label="GeneratingSetIsComplete">
<P/>
<#Include Label="SiftOneLevel">[grpchain]!{for chains of subgroups}
<#Include Label="Sift">[grpchain]!{for chains of subgroups}
<#Include Label="SizeOfChainOfGroup">
<#Include Label="TransversalOfChainSubgroup">
<#Include Label="ChainStatistics">
<#Include Label="HasChainHomomorphicImage">
<#Include Label="ChainHomomorphicImage">
<P/>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Stabiliser chain subgroups">
<Heading>Stabiliser chain subgroups</Heading>

<#Include Label="BaseOfGroup">
<#Include Label="ExtendedGroup">
<#Include Label="StrongGens">
<#Include Label="ChainSubgroupByStabiliser">
<#Include Label="OrbitGeneratorsOfGroup">
<P/>
<#Include Label="RandomSchreierSims">
<#Include Label="ChangedBaseGroup">
<P/>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Hom coset chain subgroups">
<Heading>Hom coset chain subgroups</Heading>

<#Include Label="ChainSubgroupByHomomorphism">
<#Include Label="ChainSubgroupByProjectionFunction">
<#Include Label="QuotientGroupByChainHomomorphicImage">
<#Include Label="ChainSubgroupQuotient">
<P/>
<#Include Label="MakeHomChain">
<P/>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Direct product chain subgroups">
<Heading>Direct product chain subgroups</Heading>

<#Include Label="ChainSubgroupByDirectProduct">
<#Include Label="ChainSubgroupByPSubgroupOfAbelian">
<P/>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Trivial chain subgroups and sift function chain subgroups">
<Heading>Trivial chain subgroups and sift function chain subgroups</Heading>

<#Include Label="ChainSubgroupByTrivialSubgroup">
<#Include Label="ChainSubgroupBySiftFunction">
<P/>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->
<P/>
</Section>
</Chapter>

