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

N. Yang, A. A. Buturlakin

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