（I）Niipotency of the Soluble Radical of a finite Group Isospectral to a simple Group
讲座题目：Niipotency of the Soluble Radical of a finite Group Isospectral to a simple Group
主 讲 人：Andrey Vasilyev 教授、研究员
We refer to the set of the orders of elements of a finite group as its spectrum and say that groups are isospectral if their spectra coincide. We prove that the solvable radical of an unsolvable finite group isospectral to a finite simple group must be nilpotent.
（II）The Baer-Suzuki theorem for the π-radical
讲座题目：The Baer-Suzuki theorem for the π-radical
主 讲 人：Danila Revin 教授
The famous Baer-Suzuki theorem states:
Let p be a prime. Then a conjugacy class D in a finite group G generates a p-group
(equivalently, belongs to the p-radical of G) if and only if every two elements of G generate a p-group.In this theorem, one can not replace the prime p with a set π of prime. In the talk, we discuss the following result obtained in a joint work with Yang Nanying and Evgeny Vdovin. Let π be a prime. Then there exists a constant m depending on pi with the following property. A conjugacy class D in a finite group G generates a π-group (equivalently, belongs to the π-radical of G) if and only if every m elements of G generate a π-group.