We devised a function in class to test if the nilpotency class of a group is or not the sum of those of its p-Sylows. The original was the first one below, without the n:=NilpotencyClass(G) line. I got a strange result, as you will see below. The teacher got a different strange result: 3 1. But the group G wasn't abelian, so we would have found a non-Abelian class 1 nilpotent group, which is absurd. Then we tried isolating the function, also because a classmate of mine had the function properly working. That solved the problem. Curious about this mystery, I tried to isolate the problem, and found it came straight out of the function. I tried calculating the returned NilpotencyClass at the start of the function and it worked. If I don't, even outside the function I still get NilpotencyClass(G)=32767! So I have the following code:
TestNilpotencyClass := function(G)
n:=NilpotencyClass(G);
if not IsNilpotent(G) then
return 0;
end if;
N := #G;
somma := 0;
for pn in Factorisation(N) do
p := pn[1];
P := SylowSubgroup(G,p);
c := NilpotencyClass(P);
somma +:= c;
end for;
return somma, n;
end function;
TestNilpotencyClassb := function(G)
if not IsNilpotent(G) then
return 0;
end if;
NilpotencyClass(G);
N := #G;
somma := 0;
for pn in Factorisation(N) do
p := pn[1];
P := SylowSubgroup(G,p);
c := NilpotencyClass(P);
somma +:= c;
end for;
return somma, NilpotencyClass(G);
end function;
TestNilpotencyClassc := function(G)
if (not IsNilpotent(G)) then
return 0;
end if;
NilpotencyClass(G);
N := #G;
somma := 0;
for pn in Factorisation(N) do
p := pn[1];
P := SylowSubgroup(G,p);
c := NilpotencyClass(P);
somma +:= c;
end for;
return somma, NilpotencyClass(G);
end function;
TestNilpotencyClassd := function(G)
if (not (IsNilpotent(G))) then
return 0;
end if;
NilpotencyClass(G);
N := #G;
somma := 0;
for pn in Factorisation(N) do
p := pn[1];
P := SylowSubgroup(G,p);
c := NilpotencyClass(P);
somma +:= c;
end for;
return somma, NilpotencyClass(G);
end function;
G:=SmallGroups(40)[11];
TestNilpotencyClass(G);
TestNilpotencyClassb(G);
TestNilpotencyClassc(G);
TestNilpotencyClassd(G);
Loading this on MAGMA yields the following result:
3 2
32767
3 32767
32767
3 32767
32767
3 32767
Where is that 32767 coming from? Notice how it is 2^(15)-1. Why is this miscalculation being produced?
Update: I tried copy-pasting the code to MAGMA and the result was the same. Furthermore, after quitting and reopening, I tried copy-pasting only the first function, then computing the NilpotencyClass, then using the function, and here's the result:
host-001:~ michelegorini$ magma
Magma V2.20-4 (STUDENT) Fri Dec 19 2014 17:29:45 [Seed = 1006321001]
Type ? for help. Type <Ctrl>-D to quit.
TestNilpotencyClass := function(G)
n:=NilpotencyClass(G);
if not IsNilpotent(G) then
return 0;
end if;
N := #G;
somma := 0;
for pn in Factorisation(N) do
p := pn[1];
P := SylowSubgroup(G,p);
c := NilpotencyClass(P);
somma +:= c;
end for;
return somma, n;
end function;> TestNilpotencyClass := function(G)
function> n:=NilpotencyClass(G);
function> if not IsNilpotent(G) then
function|if> return 0;
function|if> end if;
function> N := #G;
function> somma := 0;
function> for pn in Factorisation(N) do
function|for> p := pn[1];
function|for> P := SylowSubgroup(G,p);
function|for> c := NilpotencyClass(P);
function|for> somma +:= c;
function|for> end for;
function> return somma, n;
function> end function;
> G:=SmallGroups(40)[11];
> TestNilpotencyClass(G);
3 2
> NilpotencyClass(G);
32767
> TestNilpotencyClass(G);
3 32767
> TestNilpotencyClass(SmallGroups(40)[11]);
3 2
> NilpotencyClass(SmallGroups(40)[11]);
2
