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4-23吴文俊数学重点实验室代数学系列报告之127【Danila Revin】
报告题目:On the existence of finite groups with non-isomorphic Hall P-subgroups

报告人:Danila Revin 教授(俄罗斯科学院,Sobolev数学研究所)

时间:4月23日(周一)下午4:20--5:10

地点:管理科研楼数学学院1518教室

摘要: Let P be a set of primes. P. Hall proved that, for a finite group, the solvability is equivalent to the existence of a Hall P-subgroup for all sets of primes P. Moreover, in a solvable group, every two Hall P-subgroups are conjugate. In a non-solvable group, Hall P-subgroups are non-conjugate in general. For example, GL(3,2) contains non-conjugate Hall {2,3}-subgroups (but they are conjugate by an automorphism). There are sets P such that, in any finite group, all Hall P-subgroup are conjugate (in particular, they are isomorphic). In the talk, we prove that, for a set P, the existence of a group with non-conjugate Hall P-subgroups is equivalent to the existence of a group with non-isomorphic Hall P-subgroups.

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