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Enhance HasXXFactorGroup #1066

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merged 1 commit into from
Feb 15, 2017
Merged

Enhance HasXXFactorGroup #1066

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35 changes: 31 additions & 4 deletions lib/grp.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -5059,6 +5059,9 @@ InstallMethod( KnowsHowToDecompose,
##
InstallGlobalFunction(HasAbelianFactorGroup,function(G,N)
local gen;
if HasIsAbelian(G) and IsAbelian(G) then
return true;
fi;
Assert(2,IsNormal(G,N) and IsSubgroup(G,N));
gen:=Filtered(GeneratorsOfGroup(G),i->not i in N);
return ForAll([1..Length(gen)],
Expand All @@ -5070,11 +5073,29 @@ end);
#M HasSolvableFactorGroup(<G>,<N>) test whether G/N is solvable
##
InstallGlobalFunction(HasSolvableFactorGroup,function(G,N)
local s,l;
local gen, D, s, l;

if HasIsSolvableGroup(G) and IsSolvableGroup(G) then
return true;
fi;
Assert(2,IsNormal(G,N) and IsSubgroup(G,N));
s := DerivedSeriesOfGroup(G);
l := Length(s);
return IsSubgroup(N,s[l]);
if HasDerivedSeriesOfGroup(G) then
s := DerivedSeriesOfGroup(G);
l := Length(s);
return IsSubgroup(N,s[l]);
fi;
D := G;
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Hmm, seems my earlier comment on this got lost? I suggested to check HasDerivedSeriesOfGroup here and if true, fallback to the previous code, which could be more efficient here. Thinking about it now, though, I think it might be faster in some cases but could also be slower in others... hmmm

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It does make sense in that case to check whether the last term of the derived series of G is in N, even if it might be slower in rare situations. Anyway, added to the commit, force pushed.

repeat
gen:=Filtered(GeneratorsOfGroup(D),i->not i in N);
if ForAll([1..Length(gen)],
i->ForAll([1..i-1],j->Comm(gen[i],gen[j]) in N)) then
return true;
fi;
D := DerivedSubgroup(D);
until IsPerfectGroup(D);
# this may be dangerous if N does not contain the identity of G
SetIsSolvableGroup(G, false);
return false;
end);

#############################################################################
Expand All @@ -5083,10 +5104,16 @@ end);
##
InstallGlobalFunction(HasElementaryAbelianFactorGroup,function(G,N)
local gen,p;
if HasIsElementaryAbelian(G) and IsElementaryAbelian(G) then
return true;
fi;
if not HasAbelianFactorGroup(G,N) then
return false;
fi;
gen:=Filtered(GeneratorsOfGroup(G),i->not i in N);
if gen = [] then
return true;
fi;
p:=First([2..Order(gen[1])],i->gen[1]^i in N);
return IsPrime(p) and ForAll(gen{[2..Length(gen)]},i->i^p in N);
end);
Expand Down
62 changes: 62 additions & 0 deletions tst/testinstall/grpperm.tst
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@@ -0,0 +1,62 @@
gap> START_TEST("grpperm.tst");
gap> G := Group((1,2),(1,2,3,4));;
gap> HasAbelianFactorGroup(G,G);
true
gap> HasElementaryAbelianFactorGroup(G,G);
true
gap> HasSolvableFactorGroup(G,G);
true
gap> N := Group((1,2)(3,4),(1,3)(2,4));;
gap> HasAbelianFactorGroup(G,N);
false
gap> HasElementaryAbelianFactorGroup(G,N);
false
gap> HasSolvableFactorGroup(G,N);
true
gap> IsAbelian(N);
true
gap> HasAbelianFactorGroup(N, Group((1,2)));
true
gap> IsElementaryAbelian(N);
true
gap> HasElementaryAbelianFactorGroup(N, Group((1,2)));
true
gap> N := Group((1,2)(3,4),(1,2,3));;
gap> HasAbelianFactorGroup(G,N);
true
gap> HasElementaryAbelianFactorGroup(G,N);
true
gap> HasSolvableFactorGroup(G,N);
true
gap> IsSolvable(G);
true
gap> HasSolvableFactorGroup(G,N);
true
gap> F := FreeGroup("x","y");; x := F.1;; y:=F.2;;
gap> G := F/[x^18,y];;
gap> HasElementaryAbelianFactorGroup(G, Group(G.1^2));
true
gap> HasElementaryAbelianFactorGroup(G, Group(G.1^3));
true
gap> HasElementaryAbelianFactorGroup(G, Group(G.1^6));
false
gap> HasElementaryAbelianFactorGroup(G, Group(G.1^9));
false
gap> HasSolvableFactorGroup(SymmetricGroup(5), Group(()));
false
gap> HasSolvableFactorGroup(SymmetricGroup(5), SymmetricGroup(5));
true
gap> HasSolvableFactorGroup(SymmetricGroup(5), AlternatingGroup(5));
true
gap> HasSolvableFactorGroup(AlternatingGroup(5), AlternatingGroup(5));
true
gap> cube := Group(( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19),( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35),(17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11),(25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24),(33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27),(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40) );;
gap> HasSolvableFactorGroup(cube, Center(cube));
false
gap> HasSolvableFactorGroup(cube, DerivedSeriesOfGroup(cube)[2]);
true
gap> G := SylowSubgroup(SymmetricGroup(2^7),2);;
gap> N := Center(G);;
gap> HasSolvableFactorGroup(G,N);
true
gap> STOP_TEST( "grpperm.tst", 1);