Gradients of sequences of subgroups in a direct product

Nikolay Nikolov, Zvi Shemtov, Mark Shusterman

For a sequence $\{U_n{\}}_{n=1}^{\infty }$ of finite index subgroups of a direct product $G=A\times B$ of finitely generated groups, we show that $$\lim_{n \to \infty} \frac{\min\{…