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<!-- %% -->
<!-- %A  quogphom.xml               GAP documentation               Gene Cooperman -->
<!-- %A                                                      and Scott Murray -->
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<!-- %Y  (C) 2000 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y  Copyright (C) 2002 The GAP Group -->
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<Chapter Label="Quotient groups by homomorphisms">
<Heading>Quotient groups by homomorphisms (preliminary)</Heading>

<#Include Label="[1]{quogphom}">
<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/>
<#Include Label="IsHomCoset">
<#Include Label="IsHomCosetToPerm">
<#Include Label="IsHomCosetToPermRep">
<#Include Label="IsHomCosetToMatrix">
<#Include Label="IsHomCosetToMatrixRep">
<#Include Label="IsHomCosetToFp">
<#Include Label="IsHomCosetToFpRep">
<#Include Label="IsHomCosetToTuple">
<#Include Label="IsHomCosetToTupleRep">
<#Include Label="IsHomCosetToAdditiveElt">
<#Include Label="IsHomCosetToAdditiveEltRep">
<#Include Label="IsHomCosetToObjectRep">
<P/>
It also has one property for each kind of source.
<#Include Label="IsHomCosetOfPerm">
<#Include Label="IsHomCosetOfMatrix">
<#Include Label="IsHomCosetOfFp">
<#Include Label="IsHomCosetOfTuple">
<#Include Label="IsHomCosetOfAdditiveElt">
<P/>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Creating hom cosets and quotient groups">
<Heading>Creating hom cosets and quotient groups</Heading>

<#Include Label="HomCoset">
<#Include Label="HomCosetWithImage">
<#Include Label="QuotientGroupHom">
<#Include Label="QuotientGroupByHomomorphism">
<#Include Label="QuotientGroupByImages">
<#Include Label="QuotientGroupByImagesNC">
<P/>
</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Operations on hom cosets">
<Heading>Operations on hom cosets</Heading>

<#Include Label="Homomorphism">[quogphom]!{for quotient groups by homomorphisms}
<#Include Label="SourceElt">
<#Include Label="ImageElt">
<#Include Label="CanonicalElt">
<#Include Label="Source">
<#Include Label="Range">
<#Include Label="ImagesSource">
<P/>

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<!-- %E -->
<P/>
</Section>
</Chapter>

