The sets of element orders of almost simple groups of Lie type
报告人：Maria Grechkoseeva(Sobolev Institute of Mathematics)
时间：2026-09-01 14:30-15:30
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.
