A generalization of the Arad--Ward theorem on Hall subgroups

N. Yang, A. A. Buturlakin

For a set of primes $\pi$, denote by $E_{\pi }$ the class of finite groups containing a Hall $\pi$-subgroup. We establish that $E_{{\pi }_1}\cap E_{{\pi }_2}$ is contained in $E_{{\pi }_1\cap {\pi }_2}$. As a c…