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#(C) Graham Ellis, 2005-2006
#####################################################################
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));
if Length(GensSeries[Length(GensSeries)])=0 then
GensSeries[Length(GensSeries)]:=[Identity(arg[1][1])]; fi;
else GensSeries:=StructuralCopy(arg[1]);
fi;
if not Order(Group(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]:=Group(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:=[];
Res[2]:=ResolutionFiniteGroup(GensQ[2],n,tietze,Charact);
#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);
od;
return Res[Length(Res)];
end);
#####################################################################
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