October 12, 2023

A Note on Thompson Problem

In this talk, we discuss Thompson’s problem* and prove that if two finite groups G and H have isomorphic Burnside rings, then G and H are the same order type groups, and give an example to show that the Burnside rings of the same order type groups are not necessarily isomorphic. *Thompson’s Problem. Suppose G_1 and G_2 are groups of the same order type. Suppose also that G_1 is solvable. Is it true that G_2 is also necessarily solvable?

About the speaker

Professor Wujie Shi, distinguished professor of Chongqing University of Arts and Sciences. Research Interests include group theory and finite simple groups and their applications in math phys. Supervised over 40 graduate students and postdocs. He is the PI of 11 grants of the National Natural Science Foundation of China and published more than 200 papers with more than 1200 citations by ~380 authors. Oner of his achievements on finite groups by "two orders" was named after his name with great influence in the world, which was affirmed by the famous mathematician Prof. J.G. Thompson. He served on “Journal of Group Theory” as founding editorial board member. He won many awards including China national and statewide, e,g, the 1st class prize of Sichuan Science and Technology Progress Award.