Actually, it turns out that may be 0 for some .
For example: a finite group is not cyclic iff .
Hello all. I have something in which there must be a contradiction but I cannot find it.
So let be the usual Euler phi/totient function, and let be a finite group. Then we have
where = the number of cyclic subgroups of order and = the number of elements of order in .
Then we also have the theorem
But I have a theorem in my notes
which states . But by (1), this is equivalent to the statement .
But doesn't this contradict (2) ? Unless which cannot be true otherwise there would be no point looking at . Can anyone help?