20.99 (2022)

Conjecture: Let $a_1 G_1, \dots, a_k G_k$, $k > 1$, be finitely many pairwise disjoint left cosets in a group $G$ with $[G : G_i] < \infty$ for all $i = 1, \dots, k$. Then $\text{gcd}([G : G_i], [G : G_j]) \geqslant k$ for some $1 \leqslant i < j \leqslant k$.