On the inheritance of $\pi$-Sylow theorem by subgroups of classical groups

Let $\pi$ be some set of prime numbers. A finite group is called a $\pi$-group if all the prime divisors of its order belong to $\pi$. Following Wielandt, it is said that the $\pi$-Sylow theorem is true for a finite group $G$ if in $G$ all maximal $\pi$-subgroups are conjugate; if the $\pi$-Sylow theorem is true for every subgroup of $G$, then it is said that the strong $\pi$-Sylow theorem is true for $G$. It is known that the strong $\pi$-Sylow theorem is true for a group if and only if it is true for every non-Abelian compositional factor of this group. The question of which finite simple non-Abelian groups the strong $\pi$-Sylow theorem is true was posed by Wielandt in 1979. By now, the answer is known for sporadic and alternating groups and Lie type groups of rank 1. The report will discuss new ideas for solving this problem for classical Lie type groups.

The talk will be streamed through “Kontur Talk”: https://imsoran.ktalk.ru/ogsac0ijeetj