On identities in the products of group varieties

Nicholas Boatman, Alexander Olshanskii

Let ${\mathcal{B}}_n$ be the variety of groups satisfying the law $x^n=1$. It is proved that for every sufficiently large prime $p$, say $p>10^{10}$, the product ${\mathcal{B}}_p{\mathcal{B}}_p$…