（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

讲座时间：2019年04月10日15:25-15:55

讲座地点：1教1B201

讲座内容简介：

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

讲座时间：2019年04月10日16:00-16:30时

讲座地点：1教1B201

讲座内容简介：

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.

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