中俄数学中心讨论班——The sets of element orders of almost simple groups of Lie type

• 主讲人：Maria Grechkoseeva (Sobolev Institute of Mathematics)
• 时间： 2026-09-01 14:30 - 2026-09-01 15:30
• 地点： Zhihua Building 413

 

Abstract：The problem of recognition of finite simple groups by element orders gave rise to the following Problem 1: for every finite simple group $L$ of Lie type and every $G$ such that $L\leq G\leq Aut L$, find the set of element orders of $G$.
By Steinberg's theorem, every automorphism of a simple group of Lie type is a product of inner, diagonal, field and graph automorphisms. By Shintani descent, Problem 1 can be reduced to Problem 2:  for every finite simple group $L$ of Lie type and every automorphism  $\alpha$ of $L$, which is a product of inner, diagonal and graph automorphisms, find the set of orders of elements in the coset $L\alpha$. I will talk about the reduction of Problem 1 to Problem 2 and what is known on Problem 2.