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#Classification of groups of order pq
####The following functions contribute to AllSOTGroups, NumberOfSOTGroups, and SOTGroup, respectively.
##############################################
SOTRec.allGroupsPQ := function(p, q)
local abelian, nonabelian, s;
####
Assert(1, p > q);
Assert(1, IsPrimeInt(p));
Assert(1, IsPrimeInt(q));
####
## typ pq
abelian := [ [p, q] ];
if not (p - 1) mod q = 0 then
s := [SOTRec.groupFromData(abelian)];
return s;
else
## typ Dpq
nonabelian := [ [q, p], [2, 1, [2, Int((Z(p))^((p-1)/q))]] ];
s := [SOTRec.groupFromData(nonabelian),SOTRec.groupFromData(abelian)];
fi;
return s;
end;
##############################################
SOTRec.NumberGroupsPQ := function(p, q)
local w;
####
Assert(1, p > q);
Assert(1, IsPrimeInt(p));
Assert(1, IsPrimeInt(q));
####
w := 1 + SOTRec.w((p - 1), q);
return w;
end;
##############################################
SOTRec.GroupPQ := function(p, q, i)
local all, G;
####
Assert(1, p > q);
Assert(1, IsPrimeInt(p));
Assert(1, IsPrimeInt(q));
####
all := [ [ [p, q] ] ];
if (p - 1) mod q = 0 then
Add(all, [ [q, p], [2, 1, [2, Int((Z(p))^((p-1)/q))]] ], 1);
fi;
if i < 2 + SOTRec.w((p - 1), q) then
G := SOTRec.groupFromData(all[i]);
fi;
return G;
end;
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