Let $G$ be a finite group and $p\mid |G|$ be prime. Can $G$ have exactly $p-1$ elements of order $p$? (except trivial groups which are isomorphic to $\Bbb Z_p$)
I remember something similar to it. I don't remember exactly the conditions. it said either there's no elements of order $p$ or there's at least $2p-2$ elements. I'm trying to find the exact conditions.
Do you rememeber any theorem with a similar statement?