Abelian groups and Sylow-subgroups For a finite group $G$, if the number of all Sylow p-Subgroups is one, then, $G$ is abelian, right? My question is, whether the other direction is also true.
Well, like Bernard pointed out even the first direction is false but if you put nilpotent instead of abelian then it is true in both direction.
Well, like Bernard pointed out even the first direction is false but if you put nilpotent instead of abelian then it is true in both direction.