Robert W. van der Waall

The classification of the finite groups whose abelian subgroups of equal prime power order are conjugate

Let $G$ be a finite group and assume $p$ is a prime dividing the order of $G$. Suppose for any such $p$, that every two abelian $p$-subgroups of $G$ of equal order are conjugate. The structure of such a group $G$ has been settled in this article.