报告题目：On the generalized p-supersolvable residual

主 讲 人：于浩然   讲师

报告时间：4月16日（周二）下午16:00--17:00

报告地点：数理楼221

报告摘要：In the 1960s, Atiyah posed an interesting problem. In 1964, using cohomology, Tate gave a positive answer to Atiyah's problem. Since then, many group theorists, including Huppert, Thompson, Roquette, Brandis, Berkovich, Isaacs and Gagola, have conducted in-depth research on Tate's Theorem. In this talk, by developing the strategy of Gagola and Isaacs, we not only prove some new results, but also use the most basic theory of transfer homomorphism to make a unified approach to many deep theorems which were originally proved by different methods. The residuals play an important role in our work. By our results, we also answer a problem posed by Murray and Tent. Then we introduce a new subgroup, namely, the generalized p-supersolvable residual. We combine the generalized p-supersolvable residual with the generalized normal subgroups, and study the generalized normality from a different view. We obtain some new results and establish the connections of these results. Our results generalize and simplify a large number of existing results.