[GAP Forum] Right Multiplication Group of normalized right loop

[vipul kakkar]

Dear GAP forum

Let me first tell you the notations then i tell you what i need with gap to
do..
Let g be a group, u be its subgroup and s be right transversal of u in g
which always contains identity from trivial coset i.e. s is a nomalized
right transversal. This will induce a normalized right loop structure on s.

Now i have a gap program which calculate all the normalized right
transversals of u in g. In addition i have two other programs "program2" and
"program3" given as follows (i have not written any of one, i know little
about gap)
----------------------------------------------------------------------------------

"program2"

i:=1;;
T:=[];
while i<=Length(s) do
T[i]:=[];
i:=i+1;
od;
i:=1;
while i<=Length(s) do
for x in s[i] do
for y in s[i] do
for z in u do
if y*x*z in s[i] then
xoy:=y*x*z;
fi;
od;
Add(T[i], xoy);
od;
od;
i:=i+1;
od;
Print("Multiplication Table for Transversals \n");
i:=1;
while i<=Length(s) do
Print(T[i], "\n");
i:=i+1;
od;
b:=[1..Length(T)];
i:=1;
while i<=Length(T) do
b[i]:=[1..Length(rt)];
i:=i+1;
od;
i:=1;
while i<=Length(T) do
j:=1;
while j<=Length(T[i]) do
b[i][j]:=ShallowCopy(T[i][j]);
j:=j+1;
od;i:=i+1;
od;
---------------------------------------------------------------------------
                                        "program3"

map:=function(arg)
local x,y,z;
x:=1;
z:=1;
while x<=Length(rt) do
z:=T[i][x];
y:=1;
while y<=Length(T[i]) do
if z=T[i][y] then
T[i][y]:=x;
fi;
y:=y+1;
oh
od;
x:=x+1;
od;
return(T[i]);
end;
Print("List of Canonical multiplication table in same order \n");
i:=1;
while i<=Length(T) do
map(T[i]);
w:=Length(rt);
sub:=[1..w];
j:=1;
T[i]:=List([1..Length(T[i])/w],j->T[i]{(j-1)*w+sub});
Print(T[i],"\n");
i:=i+1;
od;

--------------------------------------
now "program2" calculate normalized right loop table in terms of elements of
s and "program3" turn it into canonical table i.e. in terms of 1,2.......
Now i want to calculate the Right Multiplication Group of normalized right
loop, i.e.  the group generated by the right translations, this is simply
the group generated by the columns of canonical table when viewed as
permutations. i do'nt have  any idea to calculate this in gap.

Kindly help me for this problem.

with regards.
vipul