21.26 (2026)

(F. Lisi, L. Sabatini). Let $G$ be a non-trivial finite group and let $p_1, \dots, p_k$ be the distinct prime divisors of $|G|$. For each $i$, let $H_i$ be a Sylow $p_i$-subgroup of $G$. Is it true that there exists an element $x \in G$ such that for all $i$ the subgroup $H_i \cap H_i^x$ is inclusion-minimal in $\{H_i \cap H_i^g \mid g \in G\}$?