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# Any kG-homomorphism f from kG^r to another kG-module
# is determined by the images
# f(1,0,...,0), f(0,1,...,0), f(0,0,...,1)
# and the action of kG on the target.
# Given all this information, this function
# extends ("lifts") f to a homomorphism.
InstallGlobalFunction(LiftHom,function(L,R,p)
# L is a list of the actions of the g-1's
# on the target for all g in Pcgs(G).
# R is the list of images of the map constructed.
# p is the PrimePGroup of G
local n,l,m,t,j,k,first,last,jg;
n:=Size(R[1])/Size(L[1]); # Number of block columns in target
l:=Size(L); # Size of Pcgs(G); ie, |G|=p^l
m:=[];
for t in [1..Size(R)] do
Append(m,[R[t]]);
for j in [1..l] do
for k in [1..p-1] do
first:=(t-1)*p^l+(k-1)*p^(j-1)+1;
last:= (t-1)*p^l+ k *p^(j-1) ;
Append(m,ActDiagonally(m{[first..last]},L[j]));
od;
od;
od;
ConvertToMatrixRep(m,p);
return m;
end
);
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