报告题目：On the Burness-Giudici Conjecture

报告人：杜少飞

报告时间:2022.11.8(周二)19:00-21:00

腾讯会议:4789106665

报告摘要：Let G be a permutation group on a set Ω. A subset ofΩis a base for G if its pointwise stabilizerin G is trivial. By b(G) we denote the size of the smallest base of G. Every permutation group withb(G) = 2 contains some regular suborbits. It was conjectured by Burness-Giudici in [1] that every primitivepermutation group G with b(G) = 2 has the property that for any α,β∈Ω,Ω(α)∩Ω(β) is an emptyset,where Ω(α) andΩ(β) are respectively the union of all regular suborbits of G relative to α and β. In [1], anaffirmative answer of the conjecture has been shown for many sporadic simple groups and some alternativegroups, but it is still open for simple groups of Lie-type. The first candidate of infinite family of simplegroups of Lie-type we should work on might be PSL(2,q), where q ≥ 5. In this talk, we present thecorrectness of the conjecture for all the primitive groups with socle PSL(2,q).

References

[1] T. C. Burness and M. Giudici, On the Saxl graph of a permutation group, Math. Proc. CambridgePhilos. Soc., 168 (2020), 219-248.

报告人简介:杜少飞，首都师范大学数学科学学院教授。1996年在北京大学获得博士学位，师从徐明曜教授，研究方向为有限群与组合结构。1999年破格教授，并于2002年任博士生导师。近30年来，在半对称图、图的正则覆盖、正则地图、图的Hamilton圈以及其它有限群论和代数组合问题上做了大量工作，在包括J. Comb Theory Ser. B、 J. Comb Theory Ser. A、 Combinatorica、 J. Algebra及Comm. in Algebra在内的国际组合数学和代数学等权威杂志上发表论文多篇。目前担任两种国外SCI期刊 J. Algeb. Comb. 和Ars Math. Contemp 的编委。到目前为止共主持了13项包括国家自然科学基金、教育部重点项目、国际合作项目等在内的科研课题。