for any group $g$, we define an equivalence relation $thicksim$ as below: [forall g, h in g gthicksim h longleftrightarrow |g|=|h|] the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$. in this paper, we give a partial answer to a conjecture raised by shen. in fact, we show that if $g$ is a nilpot...
