Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Mark FittingSubgroup and FrattiniSubgroup as nilpotent #400

Merged
merged 3 commits into from
Feb 5, 2016
Merged

Mark FittingSubgroup and FrattiniSubgroup as nilpotent #400

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
b287fae
Mark FittingSubgroup and FrattiniSubgroup as nilpotent
fingolfin Jan 21, 2016
0d94230
Increase rank of FittingSubgroup method for IsNilpotentGroup
fingolfin Jan 21, 2016
99d75cd
Add some tests for {Fitting,Frattini}Subgroup
fingolfin Jan 21, 2016
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
18 changes: 12 additions & 6 deletions lib/grp.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -990,19 +990,20 @@ InstallMethod( Exponent,
#M FittingSubgroup( <G> ) . . . . . . . . . . . Fitting subgroup of a group
##
InstallMethod( FittingSubgroup, "for nilpotent group",
[ IsGroup and IsNilpotentGroup ], 0, IdFunc );
[ IsGroup and IsNilpotentGroup ], SUM_FLAGS, IdFunc );

InstallMethod( FittingSubgroup,
"generic method for groups",
[ IsGroup and IsFinite ],
function (G)
if IsTrivial (G) then
return G;
else
return SubgroupNC( G, Filtered(Union( List( Set( FactorsInt( Size( G ) ) ),
if not IsTrivial( G ) then
G := SubgroupNC( G, Filtered(Union( List( Set( FactorsInt( Size( G ) ) ),
p -> GeneratorsOfGroup( PCore( G, p ) ) ) ),
p->p<>One(G)));
Assert( 2, IsNilpotentGroup( G ) );
SetIsNilpotentGroup( G, true );
fi;
return G;
end);

RedispatchOnCondition( FittingSubgroup, true, [IsGroup], [IsFinite], 0);
Expand All @@ -1019,7 +1020,12 @@ local m;
return G;
fi;
m:=List(ConjugacyClassesMaximalSubgroups(G),C->Core(G,Representative(C)));
return Intersection(m);
m := Intersection(m);
if HasIsFinite(G) and IsFinite(G) then
Assert(2,IsNilpotentGroup(m));
SetIsNilpotentGroup(m,true);
fi;
return m;
end);


Expand Down
5 changes: 4 additions & 1 deletion lib/grppcatr.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -134,7 +134,10 @@ InstallMethod( FrattiniSubgroup,
0,

function( G )
return Core( G, PrefrattiniSubgroup( G ) );
G := Core( G, PrefrattiniSubgroup( G ) );
Assert( 2, IsNilpotentGroup( G) );
SetIsNilpotentGroup( G, true );
return G;
end);


Expand Down
3 changes: 3 additions & 0 deletions lib/maxsub.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -346,6 +346,9 @@ local m,f,i;
f:=Core(G,NormalIntersection(f,m[i]));
fi;
od;
if HasIsFinite(G) and IsFinite(G) then
SetIsNilpotentGroup(f,true);
fi;
return f;
end);

Expand Down
48 changes: 48 additions & 0 deletions tst/testinstall/opers/FittingSubgroup.tst
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,48 @@
gap> START_TEST("FittingSubgroup.tst");

#
gap> G:=SylowSubgroup(SymmetricGroup(5),2);;
gap> HasIsNilpotentGroup(G);
true
gap> IsIdenticalObj(G, FittingSubgroup(G));
true

#
gap> G := CyclicGroup(IsPermGroup, 12);;
gap> IsIdenticalObj(G, FittingSubgroup(G));
true
gap> G := CyclicGroup(IsPcGroup, 12);;
gap> IsIdenticalObj(G, FittingSubgroup(G));
true

#
gap> List(AllSmallGroups(60), g -> Size(FittingSubgroup(g)));
[ 30, 30, 30, 60, 1, 15, 15, 15, 20, 30, 30, 30, 60 ]
gap> ForAll(AllSmallGroups(60), g -> IsNormal(g, FrattiniSubgroup(g)));
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Did you want to have FittingSubgroup here?

true

#
gap> g := SL(2,5);;
gap> f := FittingSubgroup(g);; Size(f);
2
gap> HasIsNilpotentGroup(f);
true
gap> p := SylowSubgroup(g, 2);;
gap> HasIsNilpotentGroup(p);
true
gap> HasIsNilpotentGroup(FittingSubgroup(p));
true

#
gap> g := SL(IsPermGroup,2,5);;
gap> f := FittingSubgroup(g);;
gap> HasIsNilpotentGroup(f);
true
gap> p := SylowSubgroup(g, 2);;
gap> HasIsNilpotentGroup(p);
true
gap> HasIsNilpotentGroup(FittingSubgroup(p));
true

#
gap> STOP_TEST("FittingSubgroup.tst", 1);
51 changes: 51 additions & 0 deletions tst/testinstall/opers/FrattiniSubgroup.tst
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,51 @@
gap> START_TEST("FrattiniSubgroup.tst");

#
gap> FrattiniSubgroup(SymmetricGroup(3));
Group(())
gap> FrattiniSubgroup(SymmetricGroup(4));
Group(())
gap> FrattiniSubgroup(SymmetricGroup(5));
Group(())

#
gap> FrattiniSubgroup(CyclicGroup(IsPermGroup, 3));
Group(())
gap> FrattiniSubgroup(CyclicGroup(IsPermGroup, 9));
Group([ (1,4,7)(2,5,8)(3,6,9) ])
gap> FrattiniSubgroup(CyclicGroup(IsPcGroup, 3));
Group([ ])
gap> FrattiniSubgroup(CyclicGroup(IsPcGroup, 9));
Group([ f2 ])

#
gap> List(AllSmallGroups(60), g -> Size(FrattiniSubgroup(g)));
[ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
gap> ForAll(AllSmallGroups(60), g -> IsNormal(g, FrattiniSubgroup(g)));
true

#
gap> g := SL(2,5);;
gap> f := FrattiniSubgroup(g);
<group of 2x2 matrices of size 2 over GF(5)>
gap> HasIsNilpotentGroup(f);
true
gap> p := SylowSubgroup(g, 2);;
gap> HasIsNilpotentGroup(p);
true
gap> HasIsNilpotentGroup(FrattiniSubgroup(p));
true

#
gap> g := SL(IsPermGroup,2,5);;
gap> f := FrattiniSubgroup(g);;
gap> HasIsNilpotentGroup(f);
true
gap> p := SylowSubgroup(g, 2);;
gap> HasIsNilpotentGroup(p);
true
gap> HasIsNilpotentGroup(FrattiniSubgroup(p));
true

#
gap> STOP_TEST("FrattiniSubgroup.tst", 1);