Quotient groups by homomorphisms (preliminary)
<#Include Label="[1]{quogphom}">

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.

<#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">

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">

Creating hom cosets and quotient groups
<#Include Label="HomCoset"> <#Include Label="HomCosetWithImage"> <#Include Label="QuotientGroupHom"> <#Include Label="QuotientGroupByHomomorphism"> <#Include Label="QuotientGroupByImages"> <#Include Label="QuotientGroupByImagesNC">

Operations on hom cosets
<#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">