报告题目1：An identity basis for the minimal non-finitely based involution semigroup

报告人：罗彦锋教授，兰州大学

报告时间：4月26日 9:00

报告地点：20-404

报告摘要：It is known that the five-element monoid A_0^1 with the unique involution operation * that interchanges E and F and fixes all other elements is a minimal non-finitely based involution semigroup. In this talk, we give an infinite identity basis for (A_0^1, ^*) and show that it generates a variety whose finite membership problem admits a polynomial algorithm.

报告题目2：Bases of Primitive Groups and Burness-Giudici's Conjecture

报告人：杜少飞教授，首都师范大学

报告时间：4月26日 9:25

报告地点：20-404

报告摘要：Let G be a permutation group on a set O. A subset of O is said a base of G if the pointwise stabilizer G_(O)=1. By b(G) we denote the size of the smallest base of G. Clearly, every permutation group with b(G)=2 contains some regular suborbits. It is conjectured by Burness-Giudici that every primitive permutation group G with b(G)=2 has the property that G ∩G^g≠∅, for any g∈ G, where G is the union of all regular suborbits of G relative to a.

An affirmative answer of the conjecture has been shown for many sporadic simple groups and some alternating groups, but it is still open for simple groups of Lie-type.

In this talk, some related work on bases of primitive groups and our recent results on the Burness-Giudici's conjecture for finite simple groups of Lie-type with small rank will be introduced. (Joint work with Dr Huye Chen and Weicong Li)

报告题目3：The normalizer problem of integral group rings of some classes of finite groups

报告人：海进科教授，伊犁师范大学/青岛大学

报告时间：4月26日 9:50

报告地点：20-404

报告摘要：The normalizer problem of integral group rings has been studied extensively in recent years due to its connection with the longstanding isomorphism problem of integral group rings. Class-preserving Coleman automorphisms of finite groups occur naturally in the study of the normalizer problem. Let G be a finite group with a nilpotent subgroup N. Suppose that G/N acts faithfully on the center of each Sylow subgroup of N. Then it is proved that every class-preserving Coleman automorphism of G is an inner automorphism. In addition, if G is the product of a cyclic normal subgroup and an abelian subgroup, then it is also proved that every class-preserving Coleman automorphism of G is an inner automorphism. Other similar results are also obtained in this paper. As direct consequences, the normalizer problem has a positive answer for such groups.

报告题目4：有限群的图表示问题

报告人：王登银教授，中国矿业大学

报告时间：4月26日 10:40

报告地点：20-404

报告摘要：本报告将介绍项目组近期关于“有限群的图半正则表示”的一个公开问题的研究进展。

报告题目5：T-varieties of left Ehresmann monoids

报告人：王艳慧副教授，山东科技大学

报告时间：4月26日 11:05

报告地点：20-404

报告摘要：This talk proposes to show that there is a correspondence between varieties of monoids and classes of left Ehresmann monoids that have the closure properties of varieties or quasi-varieties and show that T-proper left Ehresmann monoid are constructed by foldings of T-labelled trees, where a folding is an operation more general than a retract.

报告题目6：Nilpotent groups, solvable groups and factorizable inverse monoids

报告人：赵宪钟教授，西北大学

报告时间：4月27日 9:00

报告地点：国际交流中心215

报告摘要：In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if S = EG is a factorizable inverse monoid with semilattice E of idempotents and the group G of units such that the natural connection θ is a dual isomorphism from E to a sublattice of L(G), then any two composition subcentral (resp., central) idempotent series in S are isomorphic. It may be considered as an appropriate analogue in semigroup theory of the Jordan-H\{o}lder Theorem in group theory. Based on this, G-nilpotent and G-solvable inverse monoids are also introduced and studied. Some characterizations of the coset monoid of nilpotent groups and solvable groups are given. This extends the main result in Semigroup Forum 20: 255-267, 1980 and also provides another effective approach for the study of nilpotent groups and solvable groups. Finally, some open problems related to nilpotent groups and solvable groups are translated to semigroup theory, which may be helpful for us to solve these open problems.

报告题目7：有限群的特征标理论

报告人：钱国华教授，苏州工学院

报告时间：4月27日 9:25

报告地点：国际交流中心215

报告摘要：介绍即将出版的《有限群的特征标理论》的主要内容。

报告题目8：The structure of complemented Brace

报告人：李样明教授，广东第二师范学院

报告时间：4月27日 9:50

报告地点：国际交流中心215

报告题目：A brace B of is called a complemented brace if every subbrace of B is complemented. We discuss the structure of the complemented brace. 

报告题目9：正则Hom-群

报告人：郭继东教授，伊犁师范大学

报告时间：4月27日 10:40

报告地点：国际交流中心215

报告摘要：正则Hom-群是群的非结合性推广, 其结合律和单位元被一个双射α所扭曲。根据正则Hom-群中换位子以及第一型α-共轭的定义，得到关于正则Hom-群的性质。

报告题目10：Union of products of subgroups in finite groups

报告人：孟沆洋副教授，上海大学

报告时间：4月27日 11:05

报告地点：国际交流中心215

报告摘要：In this talk, we will introduce some interesting results about the union of two products of subgroups. Let G be a finite group and A, B, C be subgroups of G. We prove that if G is the union of AB and BC, then G = AB or G = BC. But if G is the union of BA and BC, we can not obtain that G = BA or G = BC in general. We also prove that if G is a 2-decomposed group, and G is a Sylow tower group or G is nilpotent-by-nilpotent, then G = BA ∪ BC implies that G = BA or G = BC. This is a joint work with Adolfo Ballester-Bolinches and Gil Kaplan.