چكيده فارسي :
Let $G$ be a non-abelian $d$-generator finite $p$-group of order $p^{n}$ with $|G^{ }|=p^{k}$. In 1991, Rocco prove that $|G\otimes G|\leq p^{n(n-k)}$ that depends on $n, k$. In 2016, Jafari proved that $|G\otimes G|\leq p ^{(n-1)d+2}$ that depends on $n,d$. In this paper, we obtain a new upper bound in terms of $n, k,$ and $d$. In fact, we prove $|G\otimes G|\leq p^{(n-k)^2+d(n+k-2)+4}$, for $p\neq 2$ and find the structure of all $p$-groups that attains the mentioned bound.
