http://stackoverflow.com/questions/2750 ... calculated
I will report the question in Markdown code, hoping it won't be too distorted by differences in formating code over here.
So, what is going on here? Any ideas why the Nilpotency class of that group (which should be 2) is very often evaluated to that number, which is 2^(15)-1, and was evaluated to 1 on my teacher's computer and to 2 on another one? And any ideas why the behaviour of this problem changes by saving the NilpotencyClass into a variable depending on where I do that in the code?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