On the Baer-Suzuki width of a complete class of finite groups

报告题目：On the Baer-Suzuki width of a complete class of finite groups

报告人：Danila Revin，Novosibirsk State University，Sobolev Institute of Mathematics (Novosibirsk) and Krasovskii Institute of Mathematics and Mechanics (Yekaterinburg)

报告时间：2025年11月3日（周一）14:30-15:30

报告地点：数学学院B301

内容摘要：A non-empty class X of finite groups is called complete if X is closed under taking normal subgroups, homomorphic images, and extensions. The Baer-Suzuki width BS(X) of such a class X is the smallest non-negative integer m such that, for every finite group G and its conjugacy class D, the subgroup generated by D belongs to X if and only if any m elements from D generate a subgroup belonging to X. If no such m exists, BS(X) is considered to be infinite. The concept of Baer-Suzuki width is closely related to the well-known Baer-Suzuki theorem and its generalizations. In the report, we will discuss 1) that BS(X) is always finite for any complete class X, 2) estimates of BS(X) in terms of some natural parameters of class X, and 3) open questions.

个人简介：Danila Revin is a full professor of Novosibirsk State University and a leading research fellow of Sobolev Institute of Mathematics (Novosibirsk)  and Krasovskii Institute of Mathematics and Mechanics (Yekaterinburg). His field of research is finite group theory, finite simple groups, and the theory of classes of finite groups. He is the author of about 100 research papers. Revin has resolved a number of open problems raised by such renowned experts as H. Wielandt, P. Hall and others. In particular, he solved a problem posed by Wielandt at the XIII International Congress of Mathematicians in Edinburgh in 1958, which had remained unsolved for a long time. Together with Professor Guo Wenbin from USTC, he completed Wielandt's 1963 program for classifying finite groups with a single conjugacy class of subgroups that are maximal among the subgroups of a certain complete class.