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eb60d3f
Convert documentation to GAPDoc/AutoDoc
fingolfin Aug 18, 2026
255c449
Fix minor errors in the manual
fingolfin Aug 18, 2026
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27 changes: 12 additions & 15 deletions .gitignore
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@@ -1,21 +1,18 @@
/htm/

/doc/manual.aux
/doc/manual.bbl
/doc/manual.blg
/doc/manual.dvi
/doc/manual.example-*.tst
/doc/manual.idx
/doc/manual.ilg
/doc/manual.ind
/doc/*.css
/doc/*.js
/doc/_*.xml
/doc/_main.*
/doc/chap*.html
/doc/chap*.txt
/doc/chooser.html
/doc/manual.lab
/doc/manual.log
/doc/manual.pdf
/doc/manual.six
/doc/manual.toc
/doc/tthin
/doc/tthmacros.tex
/doc/tthout
/doc/title.xml

# Output of the old plain-TeX manual; kept ignored until the leftover
# directory is removed for good.
/htm/

/gh-pages/
/tmp/
4 changes: 2 additions & 2 deletions PackageInfo.g
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Expand Up @@ -72,8 +72,8 @@ formations of finite solvable groups.",

PackageDoc := rec(
BookName := "FORMAT",
ArchiveURLSubset := ["doc", "htm"],
HTMLStart := "htm/chapters.htm",
ArchiveURLSubset := ["doc"],
HTMLStart := "doc/chap0_mj.html",
PDFFile := "doc/manual.pdf",
SixFile := "doc/manual.six",
LongTitle := "Formations of Finite Soluble Groups",
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -20,7 +20,7 @@ the GAP `pkg` directory, start GAP and use the command

## Examples

The subdirectory `grp' contains various examples of pc groups. They
The subdirectory `grp` contains various examples of pc groups. They
can be used as examples for applications of the package.


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60 changes: 0 additions & 60 deletions doc/cover.tex
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53 changes: 53 additions & 0 deletions doc/cover.xml
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<!-- W cover.tex FORMAT documentation B. Eick and C.R.B. Wright / 10-31-11 -->
<Chapter Label="Covering Subgroups">
<Heading>Covering Subgroups</Heading>
Let <M>\mathcal{X}</M> be a collection of groups closed under taking homomorphic images.
An <E><M>\mathcal{X}</M>-covering subgroup</E> of a group <M>G</M> is a subgroup <M>E</M> satisfying
<P/>
(C) <M>E \in \mathcal{X}</M>, and <M>EV = U</M> whenever <M>E \le U \le G</M> with <M>U/V \in
\mathcal{X}</M>.
<P/>
It follows from the definition that an <M>\mathcal{X}</M>-covering subgroup <M>E</M> of <M>G</M> is
also <M>\mathcal{X}</M>-covering in every subgroup <M>U</M> of <M>G</M> that contains <M>E</M>, and an
easy argument shows that <M>E</M> is an <E><M>\mathcal{X}</M>-projector</E> of every such <M>U</M>,
i.e., <M>E</M> satisfies
<P/>
(P) <M>EK/K</M> is an <M>\mathcal{X}</M>-maximal subgroup of <M>U/K</M> whenever <M>K</M> is
normal in <M>U</M>.
<P/>
Gaschütz showed that if <M>\mathcal{F}</M> is a locally defined formation,
then every finite solvable group has an <M>\mathcal{F}</M>-covering subgroup. Indeed,
locally defined formations are the only formations with this property. For
such formations the <M>\mathcal{F}</M>-projectors and <M>\mathcal{F}</M>-covering subgroups of a
solvable group coincide and form a single conjugacy class of subgroups.
(See <Cite Key="DH"/> for details.)
<Section>
<Heading>Covering Subgroups</Heading>
<ManSection>
<Oper Name="CoveringSubgroup1" Arg="G, F"/>
<Oper Name="CoveringSubgroup2" Arg="G, F"/>
<Oper Name="CoveringSubgroupWrtFormation" Arg="G, F"/>
<Description>
If <A>F</A> is a locally defined integrated formation in &GAP; and if <A>G</A> is
a finite solvable group, then the command <C>CoveringSubgroup1( <A>G</A>, <A>F</A> )</C>
returns an <A>F</A>-covering subgroup of <A>G</A>.
The function <C>CoveringSubgroup2</C> uses a different algorithm to compute
<M>\mathcal{F}</M>-covering subgroups. The user may choose either function. Experiments with large groups suggest that <C>CoveringSubgroup1</C> is somewhat faster.
<C>CoveringSubgroupWrtFormation</C> checks first to see if either of these
two functions has already computed an <A>F</A>-covering subgroup of <A>G</A> and, if
not, it calls <C>CoveringSubgroup1</C> to compute one.
<P/>
Nilpotent-covering subgroups are also called <E>Carter subgroups</E>.
</Description>
</ManSection>
<ManSection>
<Attr Name="CarterSubgroup" Arg="G"/>
<Description>
The command <C>CarterSubgroup( <A>G</A> )</C> is equivalent to
<C>CoveringSubgroupWrtFormation( <A>G</A>, Formation( "Nilpotent" ) )</C>.
<P/>
All of these functions call upon <M>\mathcal{F}</M>-normalizer algorithms as subroutines.
</Description>
</ManSection>
</Section>
</Chapter>
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