Sylow subgroups for distinct primes and intersection of nilpotent subgroups

Francesca Lisi, Luca Sabatini

Let $G$ be a finite group and let $(P_i{)}_{i=1}^n$ be Sylow subgroups for distinct primes $p_1,\dots ,p_n$. We conjecture that there exists $x\in G$ such that $P_i\cap P_i^x$ is i…