### The Hilali conjecture on product of spaces

#### S. Yokura

The Hilali conjecture claims that a simply connected rationally elliptic space $X$ satisfies the inequality $\dim (\pi_*(X)\otimes \Q ) \leqq \dim H_*(X;\Q )$. In this paper we show that for any such space $X$ there exists a positive integer $n_0$ such that for any $n \geqq n_0$ the \emph{strict inequality $\dim (\pi_*(X^n)\otimes \Q ) \leq \dim H_*(X^n;\Q )$} holds, where $X^{n}$ is the product of $n$ copies of $X$.

Tbilisi Mathematical Journal, Vol. 12(4) (2019), pp. 123-129