On the intersections of solvable Hall subgroups in finite groups

摘要

In the paper we consider the following conjecture: if a finite group $G$possesses a solvable $\pi$-Hall subgroup $H$, then there exist elements$x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\capH^t=O_\pi(G)$ holds. The minimal counter example is shown to be an almostsimple group of Lie type.