Quelle  resNormalSer.gi   Sprache: Shell

#(C) Graham Ellis, 2005-2006

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InstallGlobalFunction(ResolutionNormalSeries,
function(arg)
local 
 GensSeries,n, tietze,
 G,    #G[i] is generated by GensSeries[i].
 Q, GensQ,     #Q[i] is the group G[1]/G[i].
 GhomsQ,    #GhomsQ[i]:G[1]-->G[1]/G[i].
 L,    #L is the length of GensSeries
 Res,
 Charact,
        nohomotopy,
 i,j,g;
 
 ############################ INPUT DATA #####################
if IsGroup(arg[1][1]) then
#GensSeries:=List(arg[1],x->ReduceGenerators(GeneratorsOfGroup(x),x));
GensSeries:=List(arg[1],x->SmallGeneratingSet(x));   #Modified November 2024
 if Length(GensSeries[Length(GensSeries)])=0 then
 GensSeries[Length(GensSeries)]:=[Identity(arg[1][1])]; fi;
else GensSeries:=StructuralCopy(arg[1]);
fi;

if not Order(GroupWithGenerators(GensSeries[Length(GensSeries)]))=1 then
Add(GensSeries,[Identity(arg[1][1])]); fi;

n:=arg[2];
if Length(arg)>2 then tietze:=arg[3]; else tietze:=false; fi;
if Length(arg)>3 then Charact:=arg[4]; else Charact:=0; fi;
if Length(arg)>4 then nohomotopy:=true; else nohomotopy:=false; fi;
 ########################### DATA INPUT ######################
G:=[]; 
Q:=[]; GensQ:=[]; 
GhomsQ:=[];
L:=Length(GensSeries);


for i in [1..L] do
  G[i]:=GroupWithGenerators(GensSeries[i]);
  GhomsQ[i]:=NaturalHomomorphismByNormalSubgroup(G[1],G[i]);
  Q[i]:=Image(GhomsQ[i]);
  GensQ[i]:=[];
  for g in GensSeries[1] do
 Append(GensQ[i],[Image(GhomsQ[i],g)]);
 od;
od;

GensQ[L]:=GensSeries[1];

Res:=[];
if tietze=false and Charact=0 then
Res[2]:=ResolutionGenericGroup(Group(GensQ[2]),n);
else
Res[2]:=ResolutionFiniteGroup(GensQ[2],n,tietze,Charact);
fi;
#Res[2]:=ResolutionFiniteGroup(Group(GensQ[2]),n,tietze,Charact); 
#Changed 14/08/2019
if nohomotopy then Res[2]!.homotopy:=fail; fi;

for i in [3..L] do
Res[i]:=ResolutionFiniteExtension(GensQ[i],GensQ[i-1],Res[i-1],n,tietze);
Res[i]!.group:=GroupWithGenerators(GensQ[i]);  #Added November 2024
od;

return Res[Length(Res)];
end);
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